Beware this is going to be a long answer.(Like really long).

So this question bothered me a lot when I also spoilt my JEE exam in a spectacular fashion but scored more or less the same as you in Bitsat. Plus I had an additional option of joining B.Math in ISI and after much reconsideration and bothering my seniors at both the institutes, I joined Bits finally. However I do understand your position and state of mind, and I do know its very antagonizing to not spend your better years in the university/college you have always aspired about. I faced exactly the same scenario and let me convince you, I was mad about joining IIT before coming to Bits. I certainly took the failure upon my ego but in a very positive way. So, to amend things, I made a simple decision. I planned to take a partial drop (though in the due course I realized bits is more or less equally good).

Now, if you are adamant to tread on this hellish path, I must warn you that you ought to have a strategy and a prepared mind from day one. What other answers have indicated, with due respect, nobody has had any first hand experience at taking partial drop. I also gave JEE this year after joining Bits and have achieved a near under 500 rank(gen ofc) while managing a CGPA well above 8 at the same time. The only key factor that matters is you and you yourself. You just can’t expect to outsmart every other serious candidate in the mad race who is going to put all his focus on one goal while you will be juggling with ten others.

I can understand your concern of fulfilling your dream in an IIT but let me tell you a fact: I never prepared for JEE with the aim of studying in an IIT(Bits is at par, whether you admit it or not), but because I felt humiliated and insulted at a personal level on failing an exam I had so fondly prepared for. You need to analyze yourself on three levels:

(1) Whether you really are capable and deserving to study in an IIT and have that level of maturity to compete with the best minds in the country(provided you don’t have the fortunate cushion of reservation).

(2)Whether you are ready to not to loose any motivation and are prepared to spend the next year of your life in a very disciplined manner, bargaining on the perks and pleasures of being a freshman in the college.

(3)Whether you are emotionally strong and prepared to face the dreaded outcome of you failing in your JEE pursuit yet again and simultaneously having a below average CGPA in your college.

These points seem easy to read but incredibly difficult to accept and follow. Your point of view will change dramatically after you join college and these current aspirations of yours will become increasingly unconvincing. So you need to have a very strong motive. Unless you are absolutely sure that you can manage the stress and not loose focus in addition to stringently following the rules, you must take a drop. Remember taking a drop is always a better option than taking a partial drop. In my case, the thought process was to not to lose an year when I was getting such a good college; because even if I fail, I can still recover and remain at Bits. And please remove the notion that studying in college and completing its courses would make JEE exam easier for you, it would infact make it more difficult, as the courses you study would be largely distant extensions of your topics that you have studied in your past two years.

Also mind the fact that JEE advanced and your final compre exam at Bits would fall within a treacherously close interval(in my case it was within a span of 6 days only) and you simply can’t focus on the last 5–6 days on your JEE advanced exam because you will be busy preparing to leave the institute for the summer. That implies your syllabus must be completed, revised and mastered well before May(mine was completed during mid April). And lastly analyze yourself, are you that person who readily loses focus and can lose motivation midway for a seemingly impossible aim?

Be ready to be called a ghot by many people :P and compromise on lan gaming, anc visits and have a boring routine while your roomie and wingies will be having a blast, though you will occasionally find time for recreation. And I repeat once more that I didn’t study for JEE to leave Bits(Bits is hell too good for an institute to leave). My only aim was to correct my mistakes that I committed before and get the rank I deserved.

Now all that being said, I will tell you how I did it. Firstly, I was lucky enough to be placed with an understanding roommate. He had little stuff and I needed to bring lots of stuffs(study material mainly). So obviously since you and your roomie hold equal rights to your room , you can't spread your stuff without his consent. Plus generally you spend your 50%time with your roomie. So an unnecessarily distracting roommate would be the last thing you would need. I was also lucky that my family simultaneously shifted to Delhi due to my father’s job and that made it easy for me to import the bulky books and take leave from the college when and as I required.

Secondly, I was also very conscious of facing defeat in JEE once more and having a bad CGPA as a side effect. So I planned to score good in first semester by paying little less attention to JEE. This enabled me to score about 9.6 in first sem(B in E.G <you’ll never hear a B in EG, its that bad> and A- in Bio). But remember you will then also need to dedicate a good amount of your time to study as 9.5+ ain’t a cakewalk. I missed 9.9 by 3 marks, 1 in EG for an A- and 2 in Bio for an A . However I was then relaxed to study for JEE in sem 2 and could easily mess with my Bits studies. Plus I don't think anyone has exploited the zero attendance rule like I have :P.

Remember sem 1 is the time where your motivation will be at its lowest as JEE would still be very far away, and you would have been freshly introduced to college life and many new things which is bound to take a toll on you. So just to remain in practice, keep solving few JEE related stuff. I used to solve mechanics problems during that time and that actually helped me somewhat with the MEOW course at Bits. In addition I covered Integration and Area Under the curve also. First sem was the time when I also got derailed and actually reconsidered my decision, but I filled the form anyway.

Thirdly, limit the clubs you join. Don’t just join any club for the sake of joining unless you are genuinely interested because you will be required to dedicate a lot of your time to the club. Remember you will get enough opportunities to socialize even without joining many clubs. Departments are a little different story. You can’t join one after first sem or so(almost same with the clubs), but you will organize large scale events and will learn a lot. Make a point to join a technical club as at the end of the day, you ought to improve your skills to stand out. And bits have awesome tech teams. You shall find that out later. Avoid clubs that consume lot of your time, unless you are really interested or you are getting something good to learn from them. Try for Tedx BitsPilani also[Because I sincerely loved being part of that club :) ].

Find a peer group that encourages you to study. Best way is to go to the library and use it(you will find it astonishingly crowded at times).

Subscribe to a test series(must). I had the convenience of travelling to Delhi on Saturdays,give the 6 hour long tests on Sundays, and then returning Monday afternoons or Sunday midnight (Delhi to pilani by train=3 hours). Make your timetable at college in such a manner that you are allowed this routine and not miss on tut tests. Never ever take a tut on Saturday or Monday. I subscribed to Allen in Jan this year(was a little late). Take your notes and study material with you and ensure you have a proper coverage of all you need to study. If your study material is outdated order a new one from a reputed coaching.

Rectify the mistakes you made in the last JEE preparation. Believe it or not if you are getting a 6k rank, you never did the sufficient amount of preparation to score an under 1k rank. Read stories/interviews of successful JEE aspirants and try harder.

Formulate a proper method of studying and don't waste even a single minute, yes not even a single minute. Study smart. Always aim at maximum output,minimum effort. And please avoid using apps like youtube, it literally made me an idle idiot at one stage. Use your smartphone to study(it is an excellent device) as in to download previous papers and solving them while doing something else. You will travel a lot. Have a habit of solving 90%questions orally and within two minutes.

Remember you will NEVER get a 3 hour stretch of uninterrupted study time in college. So learn to study while walking,attending club stuff, and eating in mess. No possible routine of yours will allow to set your bioclock according to the JEE exam. I can write a lot about the actual details of my methods and how I studied and managed Bits and JEE at the same time but that would stretch the answer to ridiculous length. I drastically changed everything about me and used many unconventional methods of studying to boost up my preparation. So that answer is for a different time.

Utilize the winter break to cover your complete PCM syllabus at least once.This is a golden period(Dec-Jan). It can make or break your goal whether you are a regular bitsian or a partial dropper. Don’t waste a second of this period . Plus you will be at your home and you can do whatever you want.

Learn to balance between clubs and your studies in sem 2. Avoid as many lectures as you could and keep 100% attendance at tuts. If you think about it you can cover the entire syllabus of a course in 2 days and you will get a break during compres. I never studied a course before the final compre and still managed a decent CGPA . Plus lectures are really not that important unless you are aiming for a perfect A and you can cover a lot more in a lesser time through self study.

One really important thing: Please don’t loose hope.If you feel you can't do it and feel depressed, leave the goal without any guilt. You are more important than your JEE result. Stay away from depression. Listen to songs, talk to your parents, friends and seniors. Take care of your physical health.

I don’t think there is a need to further elongate the answer. The gist is that unless you don’t prepare like you are preparing for a under 100 rank, you can't reach your goal(whatever rank it may be) with a partial drop because it certainly makes things difficult for you. I am still pretty dissatisfied with my JEE result as I honestly could have made under 100 with a little more effort and alertness in the exam hall but at least I am very much elated with the HARD work I invested in this goal of mine. I am at least satisfied that I did try and had the courage to convert the seemingly impossible task into a decent result while not ruining anything.

So short answer after a long answer: Yeah you can prepare for JEE Advanced while at Bits Pilani. But you need to work a lot :-)