The mayor may have a workable plan. If he told everyone to evacuate now, it might cause major gridlock. He seems to indicate he will take that step in the morning.
There were studies done of the Astrodome in Houston after it was built however the engineers basically agreed that they'd have to see what happens in a real hurricane to be sure. Hurricane Alicia in 1983 passed almost over it with winds estimated at the time to be 70-80 mph and it did not suffer a scratch. The Superdome was built ten years later and looks more sturdy than the Astrodome does - its roof being one solid piece rather than hundreds of light panels. I think it will stand up in a hurricane.
The real worry is water and what happens if/when it begins filling with flood water. Is there a point at which people inside would be cutting themselves off from oxygen? Still, if I couldn't leave New Orleans, I would head for the Dome and find a spot in the upper deck. I'd probably volunteer to assist with all the disabled that would be coming in just to "pay" for staying there.
That's sort of what I did during Alicia. I spent the night in the hospital waiting area and then spent the next day mopping floors (leaks) before going home.