The problem is that the bitcoin is now still too small to do this, it needs to get a lot bigger to even be at the point to try it in my opinion.
Overall its possible but most likely it will not happen.
The chances is very slim even if you go to the future, dollar have been the money of US and they wont allow that a crypto currency to place their currency as it will weaken them and their industry.
Yeah the history of dollar is good and we can find that dollar is used and accpeted in majority of the countries, where as bitcoin is not that strong at a moment.
The history of the dollar is only known because we always had a war history with other countries.
Anyways, bitcoin is not strong to other countries, but people are slowly hearing about it. Western union is aware of bitcoin as a competitor I`m pretty sure.