No, a lot of the people you are thinking of were still turning out for Clinton, a New Democrat who professed more moderate positions. And even as a Southerner he had difficulty carrying the South in the manner Jimmy Carter did. That and by 2008 you not only had a more Liberal Generation coming into the voting booths, but many Northerners had moved into the Southern states along the Atlantic Coast, driving them towards the Democrats.
Jackson is not going to help Brown in the South even remotely.
The immigration point is a sound one. So my for my devil's advocacy for Jesse Jackson.