Few are insured in those zip codes for flood insurance. If they get money and run, the money won't be from insurance.
I was thinking more of the part that a lot of the people living in the low-income neighborhoods didn't actually own the property, and so have nothing to tie them back to New Orleans besides emotional attachments. Of course, emotional attachments can be very strong, but the New Orleans of the future will not be the New Orleans that they were attached to, and the people attachments have been scattered far and wide as well.
Again, one has to consider what motivates a low-income person to stay where they're at or to return where they left. First and foremost, economic opportunity. A lot of people don't move because they can't. They don't have the financial mobility. These people now do. People who take jobs will want to stick with them. Single mothers with kids will stay wherever they think it helps their kids - that will mostly be wherever they're relocated. People who take advantage of new education/training opportunities will stay wherever they find them. That will obviously be somewhere other than New Orleans.
A lot of them will plan to move back to New Orleans "some day" and some day will never come around, just like happens with a majority of immigrants. There kids will adapt to their new settings, or grow up in them, and they will move on. Etc, etc. Of course, a lot depends on how swiftly New Orleans gets back into swing, and my premise is that it'll take a while.
Granted, it's worth noting that a substantial portion of the refugees have been to date resettled in the armit of America (Houston) and if anything sends them fleeing back to New Orleans that may very well do it. ;^)