It would be nice, the globalization is occurring at a very fast rate right now , and btc will be the glue that sticks all countries together, in my opinion. Also people will be trying to get out of the fiat currencies they hold right now . They lose faith in their governments after a few economic crisis. This may happen, whether sooner or later...
No, it won't be a glue that sticks all country. Before start thinking that it can be a glue think about the governements first if they will allow a 2nd circulation of money. And fiat won't ever be replace by bitcoin as fiat is the basis of BTC's value. And almost everyone needs fiat as a mode of transaction as not everyone in fact only a few accepts btc. BTC needs to be recognized by law first in order to succeed in what you want with it.