If we are talking about the government using blockchain as means of cost-cutting and being more efficient I think it would benefit the poor overall and the before expense being used before can now be shifted to other projects of the government which will benefit the poor and the needy. But I don't think it will be enough to solve the poverty situation overall as I don't think that the expense being save will be big. Solving poverty will always depend on how big and how will the government manage their budget on focusing amd solving it.