Yes, definitely. Basically the original book, who's author grew up in Alabama, is meant to reflect the average southerner(Or even average American, really.) in the 60s/70s. Though due keep in mind that the book is different than the movie.
So yes, he's suppose to play off stereotypes. I've heard some people claim that the character has autism, but the character wasn't created with that in mind, most people weren't even aware of what autism was both when the book was written and when the movie was made.
Edit: I love how at one point I can be talking about ships, but then I can be talking about the subtext of Forrest Gump.