I just don't see it happening... Rex doesn't seem like he's the normal type of coach they bring in and while Rex has a great scheme it's all about creating pressure with the front guys and leaving the back end on islands at times and getting aggressive.
But if you look at the Packers games against both Rex Ryan (Jets) and Rob Ryan (Saints) this year, you'll see aggressive defenses aren't always good against good QBs, and Rob Ryan was willing and able to back off the aggressiveness and go with a conservative approach which didn't stop the Packers but did slow them down, while Rex put stayed aggressive and got burned because of it.
Rex has a great scheme but so do a number of defensive coaches in the NFL... only thing that makes Rex different is that he's a super cocky loud mouth and it's clear how that's effected the Jets... first couple of years it gave them something to build around and boosted them, but then as the players got used to it, wears off and becomes a negative.
Only than giving the players more fire under their butts, I'm not sure Rex would be any better than Capers, and Rex stubbornness to change his aggressiveness up is a negative, sometimes you need to back off and not always be aggressive.