When I flew Aeromexico Cancun-Mexico City-Montreal in 2015, I was able to check my luggage all the way through to Montreal without having to claim or re-check it in Mexico City. With an upgrade to business class on both legs, I also had lounge access in both Cancun and Mexico City. Not sure about Puerto Vallarta, but if you're flying economy on the first leg, perhaps not.
I honestly can't remember whether I cleared immigration in Cancun or in Mexico City on that trip. Sorry. I do know there is additional screening when you go to the gate for carry-ons, though. And it can be a bit slow.