If fiat currencies were replaced by bitcoin, the digital coin would become the offical world currency, but it's hard to say how it would be valued as all the countries would be using the same bitcoin.
I believe governments would find a way to have the bitcoins on their hands (confiscating?) and firstly they would start paying public employees wages based on their own calculations and decisions. They would also buy goods from local manufacturers based on their wishes. Then these people would have their own coins to spare too and inject on the domestic economy.

So you can conclude it would be a centralized universal currency ruled by central authorities. Maybe the only difference between our current system and this hypothetical one would be that governments couldn't print money from thin air anymore, like fiat currency.

Also, to manipulate foreigner economies can be much easier through an universal currency.
Maybe that is a good reason a world currency should never exist. It seems it creates only more centralization where there shouldn't be.