Its possible but it make take decades before it happen. Bitcoin may increase its value but it will have a hard time to get in the main market around the world. Maybe the whole cryptocurrency can be a good alternaternative for a fiat money but it will never be the main currency I think. Our government will always find ways to protect fiat money, but a least cryptocurrency will be accepted around the world in the future.
Yes this will happen in the future but I think not all country. Those third world country maybe its a bit difficult for them. But progressive country such as in Europe and america it can be done to them because they are already have system that can adopt easily in crypti currency format.