Even in the far fetched scenario that he's back for the playoffs it would be incredibly dumb for them to play him.
First off, you're saying that Zach Wilson, who at least publicly they have thrown support behind isn't going to be able to get it done. I personally don't think he can...but hypothetically, if the Jets ride him to the playoffs he would have earned the right to start. Aaron can assist him from the sideline and be part of it. But if you take Wilson out at that point you're admitting that he cannot be the QB of the future...which is still how they are painting it.
Second, dude is 39. The risk of him rushing back too fast getting reinjured and missing next season has to be pretty high IMO.
My hunch is they do in fact rush him back too soon. There really isn't anyone on the Jet coaching staff that will save Aaron from himself the way Beane has with Von. The man crushes that Saleh and Douglas have on Aaron may very well be what does them in at the end.