I don't think so, bitcoin is unknown for most people, so It's almost impossible atm, who know in future.
It doesn't matter how many people know what Bitcoin. Bitcoin will never come into a position where it has even the slightest chance of replacing any kind of fiat currency.
Governments won't keep staring ahead of themselves and allow Bitcoin to grow to a level where it will form a danger to their economy and banking system.
Necessary actions will be taken to prevent Bitcoin from possibly doing so. But even without that, the average Joe will not put fiat aside for Bitcoin.
They fear Bitcoin because of the fact that there is no central authority taking care of everything like the governments do, while for us Bitcoiners the decentralized aspect is one of the best things.