I've lived in the south my entire life, and as a whole, it's true that we typically say "coke" as a generic for carbonated soft drinks. However, I've never experianced anyone requesting a coke while wanting a 7-up or Orange Crush, etc... It's typically used more like saying "beer". "Let's grab a coke at the gas station" doesn't mean I want a coke, it means lets get a soft drink at the gas station. However, if I order a coke: "Waiter: And what would you like to drink? Me: A Coke." it doesn't mean I want an orange soda.