We stayed in Mardi Gras Manor pre-Katrina, the winter before. Like many N.O. timeshares, it has a lot of character. We stayed in a 2BR unit on the ground floor. It was cozy but entirely adequate for two people in a town where you tend not to hang around the unit a lot.
I don't think Katrina bothered that part of the French Quarter much. If it did, it would have been wind/rain damage rather than flooding and would have been repaired long ago.
Your biggest decision has to do with the location. It is in the residential section of the French Quarter. It is close to Esplanade, Frenchman's Street, the French Market and a bunch of restaurants and shops at that end of Decatur but probably ten blocks from the "entertainment" part of the French Quarter.
Give them a call and talk about your arrival plans. They have a very small office staff (pretty much one person) and you'll have to make arrangements for a late arrival.
If the alternative is not going to N.O., I'd take a week at MGM in a heartbeat. However, I much prefer Quarter House or Club La Pension (currently closed for renovations).
We were in N.O. last summer for Memorial Day week. It was hot but manageable. We had no rain but that doesn't mean it doesn't rain in N.O. in May/June. It can rain in N.O. anytime. MGM has a pool but it wasn't very appealing. Maybe it looks better in the summer.