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.
I used to believe that Bitcoin will die if these issues with high fees and delayed confirmations aren't solved any time sooner but I have a different perception now. With the overwhelming increase in patronage I doubt if Bitcoin will die any Sooner even if the challenges are not resolved because a lot of the new entrants are just interested in investing in Bitcoin so that they sell when the prices goes up; there are just a few that use it on the daily basis for micro payments and they are likely to encounter the delayed confirmations unlike those that have invested and holding.