I have lived in the South pretty much all of my life. Nobody calls all soda 'coke' as a blanket term in any part of Georgia, South Carolina, North Carolina, or Tennessee I've been to. Maybe some backwater regions do, but where I have experienced dialogue, 'soda' is the general term. Now, I usually order a Coke at a restaurant just assuming they have it, as Pepsi is much less common here (also I despise Pepsi), so maybe that's where this misconception comes from. That's my theory, anyway.
And yes, I have spent a fair amount of time in Atlanta. Even there, the idea of calling a beverage 'Sprite coke' is completely alien to me. There are cherry cokes, grape cokes, etc, but that's because those flavors of Coke actually do exist.
Now, if you want to hear weird, I will admit that I have heard many elderly people call Coke 'co-cola.' It might just be an antiquated colloquialism for coke that's gone out of style.