If the current situation persists for too long, then I believe yes... Bitcoin will be damaged, and the small Bitcoin holders will get out of the boat first, not before paying a premium for their transaction fee to fiat, of course.
I think its not, it will still remain even the problem in the transaction fee was not yet solved. Maybe other cryptocurrency will replaced bitcoin but i don't believe that bitcoin would die. It have already than a big part here and its not that easy to disappear only because of its problem in the transaction fee. It will be solved soon just keep waiting and trust bitcoin.