Under those circumstances, no looters would be bordering. They would either be arrested or medivac'd out if they survived.
Short answer is...no. Come with the clothes on your back and your life.
That's real easy to type from the comfort of your home and its full refrigerator. 36 hours in, and no agency is bringing in any water to these persons not in the Superdome, and it is physically impossible for many of the stranded to walk the miles through high water to the dome. There's a big difference in stealing a TV and stealing food, and this isn't the normal disaster where waters recede and help reaches them within 72 hours.
Those people are going to eliminate themselves.