"Or is that accent a cliche with little basis in reality?"
Which accent? If you listen real closely, the mayor has a tinge of the N.O. accent. The cajun accent, however, is different and is not heard often in N.O. It's certainly out there in the bayous.
"Are those people filtered out by the media?"
I think the last thing the media has time to do right now is filter out people with "unacceptable" accents.