Countries with a weak currency can greatly benefit from this. In fact, the presence and importance of Bitcoin is something that can be noticed strongly in such countries, as Venezuela.
No one wants to depend on a currency with astronomical inflation rates, and Bitcoin is one of the few affordable alternatives for a large portion of the population of such countries.
That remains to be seen
While Bitcoin can help an individual, I don't think it can help the whole country. I'd rather say it would only worsen the situation there, for example, in Venezuela. How come? The answer to this question is found in understanding why Bitcoin helps a person. It makes him better off by impoverishing the rest of the population as simple as it gets. It works in pretty much the same way as any speculative asset. The reason is simple, though, Bitcoin is not productive, i.e. it doesn't produce anything (which is what makes the wealth of a country), it only redistributes the existing wealth. That's basically why it may help an individual but hurt a country