Yes, it could be worthless, but it would take time to achieve this... many people still will continue to use fiat money for many years, before that happen.
it wouldnt be worthless for sure, because then bitcoins wouldnt still replace all the money, first of all bitcoin should grow way more i think
i also think it wont be worthless, because the bitcoin price is not depend on the fiat value, so if it goes up to 10.000$ nothing will effected except the bitcoin user, we will be richer and more people will try to keep more coin, there wont be any effect on any country