That's a nice hypothetical question.

Let's create a situation and contemplate what would happen. For the reason not to transgress, I have marked the actual words of Buddha in italics and marked a reference no pointing to the source of the same. Rest all is fiction, a built-up to the hypothetical situation as requested.

Thus, I contemplate:

Shankara walks into a hall where Buddha is stationed along with His followers. He bows down to Buddha and seeks for His good health. He then Introduces Himself as a Buddha from a millennium later and requests permission to ask a few questions.

Buddha welcomes Shankara and offers Him a high seat. Everyone in the hall is amazed to see a man from the future and looks forward to the discussion that is about to be unleashed. Equally excited are the gods (devas) who descend from the heavens to witness this discussion.

Shankara proceeds and asks a question:
"Who are you, sir?"

Buddha remains mum. A deep silence engulfs the hall with pin-drop silence. No one utters a word expecting to receive an answer from Buddha, but there is none.

Understanding that there is no answer coming, Shankara then raises another question. He asks
"Sir, who are you not?"

Buddha again remains mum. Realizing that the person on the other side is equally enlightened, He understands the trap that replying to such a question would lead to.

Pindrop silence again engulfs the hall. With no answer apparently coming, Shankara then raises the third question

He asks
"Sir, are you somebody? Or are you just a permutation and combination of matter that by accident gained consciousness and became sentient? Will the leaving of this consciousness be the end of Gautama- The Buddha?"

To this Buddha replies:
"Shankara, Consciousness does not come to a man without reason and does not pass without a reason(1). The same is true for all sentient beings, including me".

Shankara then replies,
"So Sir, it can be said that this conscious body of Gautama - The Buddha arose to your state due to certain reasons?"

"Yes you are correct Shankara" replies Buddha.

"And what sir, was the reason of this rise of consciousness in you and for that matter in all sentient beings?" asks Shankara

Buddha replies:
"Its conditional formations. What one intends, what one arranges, and what one obsesses about: This is a support for the stationing of consciousness. There being a support, there is a landing [or: an establishing] of consciousness. When that consciousness lands and grows, there is the production of renewed becoming in the future. When there is the production of renewed becoming in the future, there is future birth, aging & death, sorrow, lamentation, pain, distress, & despair. Such is the origination of this entire mass of suffering & stress. (2)

Exalted, at understanding the primary reason for existence, Shankara says:
"So Sir, basically it's us, ourselves who are responsible for what we are. What we intend, we act for, and in the process sowed the seeds of our own future formations!"

Yes Oh' Shankara, replies Buddha. "We are what we desire; we become our defining desires. Our lives have direction, and that direction is governed by our desires and aversions... What one is desiring gives rise to its appropriate identity (atta-bhàva), whether favorable or unfavourable" (3)

Shankara then says:
"So to sum up till now, we may say that a being becomes sentient because of conditional formations which in turn are formed by desires.

"Yes you may say so" replies Buddha

Then sir, says Shankara "what is it that leads to desire?"

"Its again conditional formations" replies Buddha. We are our own housebuilder. Seeking but not finding the housebuilder, (a being) travels through the round of countless births. How painful is birth over and over again? (4)

"So we are a net of these conditional formations which in turn is the station on which our consciousness stands?" re-enquires Shankara

"Yes, it's so" replies Buddha.

To this Shankara asks, "And since when, Oh Venerable sir, has this cycle of ever-repeating births been on?"

"For this one needs to get into deeper realms of one's consciousness" replies Buddha. "With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, one directs and inclines it to the knowledge of the recollection of past lives (lit: previous homes). He recollects his manifold past lives, i.e., one birth, two births, three births, four, five, ten, twenty, thirty, forty, fifty, one hundred, one thousand, one hundred thousand, many eons of cosmic contraction, many eons of cosmic expansion, many eons of cosmic contraction and expansion, [recollecting], 'There I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose there. There too I had such a name, belonged to such a clan, and had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose here.' Thus he recollects his manifold past lives in their modes and details." (5)

Thus sir, says Shankara "These conditional formations have been making us reinvent ourselves, again and again since times immemorial leading to conditional consciousness in each life.

"You are correct Shankara", replies Buddha explaining the cycle of samsara.

Shankara then enquires "Then sir, is there an end to this ever-repeating cycle of samsara"

"Yes there is", replies Buddha further adding that the key to ending this cycle is the realization of the desires that lead to further housebuilding. Once caught, it shall not build a house again. Its rafters (are thus) broken. Its ridgepole demolished. The unconditional consciousness (is thus) attained. And every kind of craving has been uprooted and destroyed. (6)

So sir says Shankara, "This means that there are two types of consciousness. First, the conditional consciousness that stations on to the conditional formations and changes as per the changing formations and second the "unconditional consciousness" that is separate from conditional formations and remains same and is discovered once all the conditional formations cease to be?"

The house suddenly turns euphoric. Where has Shankra brought Buddha to? Where is the discussion heading?

Buddha goes back into deep silence. The house waits impatiently. Buddha preached Anatta. Buddha, they thought preached against self. Here, the discussion has arrived at the existence of a state that is the same as self - "The Atta".

Seeing no response coming, Shankara then asks another question. He says:
"Sir, what's the difference between unconditional consciousness and soul".

Buddha again remains mum. Buddha does not answer any questions on self and says:

"Shankara, I Teach a doctrine that leads to abandoning the wrong assumptions of self. If (one) follows this doctrine, unwholesome mental states disappear and the states that tend to purification increase; and one realizes and remains in the full perfection and purity of wisdom here and now. (7)

Shankara had His answer. The assembly is in jubilation. The gods shower petals and as Shankara departs, the house bows down to Shankara - The Buddha from the future.

Love

PS: For more on what Buddha really meant by the term “Anatta”, I welcome you all for discussion at my below blog on Suttas on Anatta:

Buddha & the concept of Anatta

Source:
1. Potthapada Sutta
2. Cetena Sutta
3. Mahatanhasankhya Sutta
4. Dhammapada
5. Samannaphalla Sutta
6. Dhammapada
7. Potthapada Sutta