And what countries with the problem of the economy are you talking about. If for example these are African countries, then there is not everywhere an Internet to use cryptocurrencies.
Bitcoin can be useful not only for the people who are poor but also for them who is wealthy so I do not think this is for any specific country, I mean it can be useful for any parts of the globe.
Bitcoin is really useful thing, but I do not think that it is able to put the country out the pit. Bitcoin can help the country to survive, but not to build strong economics.