While they have been mentioned multiple times in the anime, and we have seen other languages in the games, I personally don't think countries exist in the Pokemon world. While it would make more sense if they were part of the countries themselves, the main disproving factor is that the Unova region looks close to nothing of the geography of the New York Metropolitan area(With the exception of Castelia and Nimbossa city). All the other regions look close to the countries they are based off of, though, so who am I to talk? Basically, I think regions substitute for countries.
Next question:
What place, state, or country would you like to see a Pokemon region based off of? I would like to see one based off of Texas, USA, as Texas has a bunch of different parts to it, Like a coastal area, a mountain area, a lush green area, and of course, a desert.