No, Sean Payton left his 1st HC job in New Orleans by his own choice, with a very sad fanbase that did not want to see him go. He has taken his second job and reignited a downhill franchise.
Mike McCarthy was fired, and then wedged out, at two different franchises and now he is interviewing in New Orleans for his 3rd try. Neither of the first two fanbases would ever ask to have him back. Square peg, round hole.