I was under the impression that bbq pits(charcoal or gas) were not allowed anywhere in the dome parking areas, but I did see a couple of people using camp stoves this season. Maybe shoot the superdome management an email?
Any type of open flame is not allowed. Since you have to have a flame to get the pit going, you can't bar-b-q or do any type of cooking. Cold cuts at a tailgating party is lame. They also have rules as to how much room you can take up. If you really want to upgrade and do it right, get out of the dome parking lot and move out to where the real tailgaters are on Loyola Ave. or Poydras past the Claiborne overpass and under the interstate.