If all countries can accepted crypto currencies in there various countries, as a means of payment and as a means of online exchanges, such as money is, money is anything use as a means of exchange and general acceptable. With the means I think all cryptocurrencies (bitcoin) will definitely go round the world, and will be use as a means of exchange. I will be so grateful to the creation of crypto currencies. This will also help our future generation, Remember something when we do international transfer across the countries, it may take a while to get the money to your local bank account, but with cryptocurrency you can get instant reflection if bitcoin etc is transfer to wallet,And you can make use of your coin (bitcoin ETC).
This analogy you posits is not something that will likely happen and even if it's going to happen, I don't see it replacing the existing fiat each country is currently utilising. The reason is simple aside the primary currency function that fiat satisfy, it still goes a step further by being an identity of the country and that is something that cannot be quantified.