Yes, I think Southern US accents are often used as shorthand for "uneducated" in film, absolutely. One of Pedro's favorite games, when he has to call and order theater tickets, for instance, is to adopt his best Good Ol' Boy voice and say something like, "Hey, y'all, I'm thinkin' I wanna come see that ol' Oprey y'all have goin,' do y'all have any tickets left for that there show?" He can lay it on pretty thick. Once, he had to call tech support, and he did the whole thing in Southern, asking more and more difficult technical questions until it became clear that the service rep didn't know jack about the product he was trying to sell. The tech didn't know what to do with this hick on the phone who sounded like the cast of Deliverance but seemed to really understand the ins and outs of jailbreaking a cell phone.
I don't recall the specifics and I'm not doing it justice here, but it was clever and funny, IMHO.
In the UK it is still the posh accents that drop postvocal R and also insert Rs between words in some cases. It's a very neat proof that what is stigmatized or admired is not actually something about language (like that dropping Rs is "lazy" or "ignorant"), but it's how people feel about the group that speaks that way, and the accent is just how the group is identified.
What's also funny of course is that Americans basically think nearly all British accents sound fancy. People who speak horribly stigmatized British accents can come here and have everyone think that how they speak is totally cool.
Maybe I watch too much BBC, but I don't think East London cockney accents sound particularly intelligent, even to most Americans. Fun to listen to and perhaps even "exotic" in a mundane kind of way, but I think most Americans with half an ear could hear the class difference between cockney and RP.
For my part, I love listening to accents in general, but my favorite lately has been Welsh. When I was watching a lot of Torchwood I loved having those sounds sloshing around in my head all the time. Apparently a lot of English speakers think it's ugly and hard to understand, but I think it's glorious. But, then, I also love listening to working-class New York accents, so what the hell do I know?