No.

Actually this is a surprisingly interesting question - I initially dismissed it but it bears some consideration. Stars don’t die (or rather move on to the next stage in their life) because they run out of hydrogen, but because they accumulate too much helium.

We often plot a graph called a Hertzsprung-Russell diagram, of luminosity against surface temperature, as above (from The Cosmic Perspective textbook series, authors Bennett, Donahue, Schneider and Voit). The sun is currently on the Main Sequence; that means due to the high temperatures in the core it is fusing hydrogen into helium. This releases energy which keeps the core hot and provides the support to resist the force of gravity pulling it inwards - all stars are in a balance between these forces; thermal pressure opposing gravity. However, the end product of the reactions is Helium, which at these temperatures is in nuclear terms inert - it won’t fuse further, and just builds up in the core.

Eventually the core gets so large and dense that the fusion can’t continue to support it and it collapses further, heating up. At this point, one of two things happen:

• If the star is too small, the core collapse triggers a pressure pulse that blows the outer layers off, leaving a dense white dwarf star to cool in the centre, surrounded by a “planetary” nebula.
• If the star is big enough, the core collapse gets so hot that the next stage of nuclear fusion can take place, and helium starts to react, producing carbon, nitrogen and oxygen as products.

In the second case this fusion generates further energy which stabilises the collapsing core. The core is much hotter so some of this heat transfers to the outer layers meaning that the star swells up to form a red giant star, which moves off the Main Sequence into the top right hand corner of the HR diagram. Actually the process then repeats; byproducts of the CNO cycle accumulate at the core which then collapses further and starts fusing to heavier elements etc etc, eventually ending at iron because it has the highest binding energy - you can’t get any more energy out by fusion beyond this point, and the star gets bigger and bigger.

Now, to come back to the question. This is not happening because the star is running out of hydrogen, but because it has accumulated too much helium. Adding more hydrogen, even if possible (what were you thinking of doing, dropping Jupiter in?) won’t change that. If anything, it would accelerate the process - larger stars age quicker, because they need to fuse hydrogen faster to support the greater weight of the outer layers.