If there was some sort of sciencey explanation for the abilities ("accellerated" cells for regeneration, electomagnetic brainwaves for telekinesis, etc.), then heck yeah! And it would filter out a lot of the characters I don't really like, since they would die off as the centuries pass. We'd be left with Sylar (WHOO!), Claire (Bleh), maybe Peter (meh), and maybe some time-traveling Hiro, if he gets better (YATTA!). Perhaps some ancient alien interference with genetic engineering is responsible for these abilities, and everyone wants to get to the bottom of it.
That would be pretty awesome! Despite my fanfiction phobia, I would definitely give this a read!