I'm against it, for two reasons:
First: the higher the character level, the more work for the character judges (without taking overhauls into account, you can assume that the sheet at level X-1 was correct and certified, and just look at the changes that were made, which are pretty minor.
Second: the point of the overhaul wasn't to take advantage of new releases (that's what the "retrain more than one feature" rules are for), it was to correct things that don't really work out in game like you'd planned when you made the character. By level 2, you should have figured these things out.
In Quagmire's case, I think he reached level 2 before we had overhauls, right? So I'd just say any character who reached level 2 before the rule change can get an overhaul before their next level-up, as a grandfather clause.