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.
Yes if the problem in the transaction fee would not be fixed or solved soon then there is a possibility that bitcoin will be die. Because it has a big effect to every user. But I believe that they are going to fixed it as soon as possible so that bitcoin will still remain and can be used even in the future.