I don't think that makes much sense. It is possible that Bitcoin reaches this value someday, but it will not make people stop using fiat. To gain more users, Bitcoin must first reach more people willing to sell goods and services for Bitcoins. In this way, there will be greater liquidity in the market, and over time Bitcoin will gain more stability. This will give more confidence for people to use Bitcoin as a currency.
People would surely use bitcoin infact they are already using it as a currency, but that would probably not make fiat worthless in any means, no matter where bitcoin reaches but people will still use fiat as long as there is governmental system in the world and that system does not seem to be vanishing at all.