Sweet tea isn't much of a thing in Texas, though that's changing slowly. The further east you go, the more common it gets. It's definitely not a required drink for a BBQ meal. And around here hushpuppies are a common side for fried seafood (especially catfish), but not BBQ. Here in Texico, potato salad, cole slaw, and pinto beans are the traditional sides. And nanner puddin for dessert, of course.
Brutus: sweetening tea with sugar packets doesn't produce the same effect, since typically sweet tea is super-saturated with the sugar while still hot, right after brewing, so it absorbs a lot more of the sugar. But like I said, it's not much of a big deal around here, and I don't personally like or drink it.