Official Georgia Dome policy is absolutely no outside food or drinks. Even a small, sealed bottle of water will get tossed by security at the gate if they find it.
In the past, bag checks haven't been "TSA style," just a quick glance into your bag. So you can probably get a package of crackers or a small bag of chips into the dome. A bag of chili dogs, onion rings, and some frosted oranges from The Varsity - No.