DR and PR have already benefitted a lot, no?
Certainly PR has because the Puerto Rican community in the US is very close. They seem to "maintain their Puerto Ricaness." And it looks like DR will benefit from Charlie Villanueva, whom I think was born in DR, actually. I'm not sure.
After those two, the English-speaking Caribbean and Haiti could find a lot of good eligible players. But none of those countries have the organization to convert that into sustained success right now.
Absolutely Haiti could benefit! Unfortunately, the whole country is a wreck, so there is no hope for any kind of athletic success.
If the immigration process and the embargo were lifted, another country that would clearly benefit is Cuba. Of course, they've got their own problems because they won't even talk to their baseball players who play in Latin American winter leagues.
Lastly, the big country that could benefit the most from populations who have immigrated to the US is Mexico. There are something like 25 million Americans with "Mexican heritage" in the US. I'm sure there are plenty of professional players, NBA players like Earl Watson, who could legitimately play for Team Mexico. I think right now they've got Adam Parada, a guard/forward from California on the NT now.
Of all the teams in the Americas though, I think Mexico is the weirdest. Given their population and the strength of their domestic league, they
should have a very competitive national team. They
should be up there with Brazil and Puerto Rico, but they never do well at the Tournament of the Americas. It's weird. They should be much better than they are.