I don't think this happens. Fiat currencies are controlled by central banks and governments and do not let this to happen. It will happen only if cryptocurrencies completely replace fiat money. The probability of this is very low.
I agree. This is possible but it is hard for cryptocurrencies to cope. Investors of bitcoin or any other cryptocurrencies are always looking for the fiat conversion.
For the sake of OP's question, yes I think it will decrease the value of fiat. People will more be concentrated on one medium and so it will decrease the other medium. Though I know the government will never let this happen.