I think not, fiat money will never be replaced by bitcoin.
because it is the tool we use for the current exchange, bitcoin is more suitable for the investment tool.
I think this thing would be happen but it will take time. If you really want to live in the future many people will accept to replace fiat as cryptocurrencies simply because it is very easy to use and you can really pay your bills easily and instantly. Furthermore, I hope that in the near future our traditional money will be still there because we can't replace and I think the best thing to do is to consider cryptocurrencies as real money.