Poverty is a strong word. To be profitable with bitcoin you need to invest in it and anyone below the poverty line who doesn't know where his next meal will come from can not possibly invest in bitcoin. Truly, bitcoin comes with a lot of opportunities to financial freedom but you still need to be able to invest.
That's to say if Bitcoin is the only option for a poor man to escape poverty, the person will eventually die in that poverty because there will never be enough money to feed, much less a spare one that could be used as a form of investment.
I think bitcoin might be able to help but not entirely because there are so many factors of poverty both from within and outside the country itself.
If you really want to solve the problem of poverty, it should have been solved decades or hundreds of years ago, but poverty is always there???
that's the question now
I necessarily don't think there can ever be a world that is fully poverty-free; there will always be poverty to some degree. The level could only be reduced, but it can't be eradicated no matter what means and how hard the government and the people try.
Bitcoin can do a lot of positive things but ending poverty, I can't say yes but it depends on how small that nation is,
Even if the country is as small as my village, the result will still be the same as what you have described. Bitcoin can't move a completely poor person or country out of poverty.