I think some industrial third world countries could survive the war if they had no nukes themselves. Sure, there's the radiation and the FEV floating around and causing mutations, and there's the climate change, and there's the lack of fossiel fuels, and there's the chaos, but after that, it's possible for a country to survive, pretty weakened, but possible.
I think that the country with the biggest possibilities of surviving the war is Brazil. (No, I'm not biased) Why Brazil?
1. Immense area of fertile land. I think that even if the climate changed, we would still have a lot of fertile land. Except in the northeast, that is. The northeast would probrably turn into a wasteland.
2. Immense Industrial Might. Brazil was already turning into a industrial country in the fifties. By 2077, Brazil was probrably a big industrial country, maybe even a first world country. This means that Brazil probrably has a big army.
3. Not being too dependent on outside imports. Sure, we import a lot of things, but if the world suddently exploded, we would't be without food or something. Since WWII, our country took measures so we could always be self-suficient in any case. The only thing we need from outside is oil.
I could imagine Brazil entering into a period of chaos with many states splittering (or not) or being invaded by Argentina. After that period of Chaos, Brazil would probrably be a NCR-sized country around the southwest constantly threatened by raiders, but armed to the teeth.
Of course, this asumption comes from the theory that South America will not turn into a arena where Brazil, Argentina (and maybe Chile) kill eachother over Bolivia's natural gas and Venezuela's oil. If war DOES break out here, then it's possibly we will just nuke each other to death. The Brazilian Governament came pretty close to making The A-Bomb during the military governament, but they shut that down after "Democracy" returned and the cold war ended. Hell, we have all the means to make a nuclear bomb today, but we don't do it because we don't want to. Same to Argentina.
Other third world countries that could survive the war include Argentina, Chile, Mexico, Mongolia and possibly Ireland.
And as for Africa... I doubt it would change much after a nuclear war... Except the climate change. And the killer mutants. And the ghouls. And the lack of europeian influence.