If you ask me, IF BTC becomes the dominant world currency, fiat would still be around BUT it would slowly base its value on BTC, rather than BTC basing its value on fiat.
That is if btc will be successful in dominating against other world currency but why do you even think of it dominating atm if Bitcoin itself has gone astray? Instead of it being used as a currency, it is seen by most of it's users as an asset. I can say this for certain because most of us here hodling bitcoin just speculates how it's price will be higher tomorrow and how we will get profit from it. That's not the proper use of a currency IMO and for btc to dominate world currency, it needs to be used in transactions more.