I've heard a theory that the slow southern accent was due to a hookworm outbreak. So maybe historically at least there was some validity in the assumption.
http://www.pbs.org/wgbh/nova/next/nature/how-a-worm-gave-the...
http://www.pbs.org/wgbh/nova/next/nature/how-a-worm-gave-the...
Personally, I think it's more related to negative opinions about the South following the Civil War, which is why even upper-class southern accents face the same stigma.
Old English is ~500AD, Beowulf, and a completely different language to anything ever spoken in the United States.
Unfortunately, I don't know the name of the book, which was very well documented, but I read a history of the Deep South at one time. It is unfortunate I can't remember the name because it documented something that flies in the face of what most people apparently believe about the Federal minimum wage law. This book asserted that it was an anti-racist policy intended to end the practice in the Deep South of paying Blacks half of what Whites made. Many Blacks were fired after it was passed because Southerners often were simply unwilling to pay Blacks "a White man's wage."
World War 2 was instrumental in making the Federal minimum wage law stick. Before that, it was proving to be a failed and unenforceable policy.
Up to half the population in the South is Black (it no doubt varies, but it is about half in the city I grew up in) and under slavery they were forbidden from learning to read and write. It was one of the ways they were controlled. So when you suddenly have something like half your population made up of freed slaves, most of whom are illiterate and who carry a lot of baggage about being forbidden from learning, yes, the area as a whole is going to lag behind the rest of the nation educationally. It will take a long time to start remedying such a deficit.
Many hot places have a reputation for being lackadaisical. In Mexico, they have a tradition of taking siestas -- naps -- during the hottest part of the day. In the Middle East, they have the expression "Only mad dogs and Englishman" to refer to who would be going about their business out of doors during the hottest part of the day.
The Deep South in the US is not only hot, it is also humid. I grew up in Georgia and I have lived in Southern California and Texas, among other places. When it is humid, you can't just drink more and sweat it out. It won't evaporate. It's like a sauna.
So the only thing that makes sense is to sit your ass down on the front porch in the shade in a rocking chair and make chit chat until it isn't so hot that doing stuff threatens to cause fainting. As a wild ass guess, this is the origin of the slow Southern drawl -- getting through the heat of the day without heat stroke, pre-AC, by slowing down and sitting a spell, during which time you didn't want to do anything too energetically, not even talk.
And then it is completely and totally normal for people to make associations that run both ways, where the Southern drawl becomes a signifier for poverty, lack of education, etc since those things were common there, though it really had nothing to do with inherent stupidity of the locals.