Well I don't think crypto alone will have the power to drag these countries to the same level of the more developed ones, but I think they will have a very important role in their economic evolution. I would not be surprised if the first places where we will see bitcoin mass adoption, will be in these poor and undeveloped countries. Most of their population don't have access to bank accounts, and bitcoin can help here. Their coins are usually poor, and have no economic power, and again, bitcoin will help them here as well. These countries will be the perfect test environment for crypto, and I'm sure their economy will have a lot to gain with this process.
What you have said is right and a perfect example is Zimbabwe. This is a country that the government has totally ridiculed its currency, that now they just had to abandon it and concentrate on making use of USD which we both know that balls down to exporting USD for usage.
However, with the low supply of USD in circulation, the government banned any form of international transactions which left some traders unable to pay merchants outside the country, banks are not allowed to make any international transfers except locally, students abroad find it hard to get their school fees paid and so on. All these made crypto the saving grace and which is why the demand is extremely high and presently trading above $13000.
https://golix.comThis shows that cryptocurrency would make them gain a lot in the long run and hopefully help the economy in a way.