Whether or not he would be cheered would all depend on how he was booked as a heel. How well it works, would depend how much WWE really puts into it, and if they were ever to pull the trigger on it, they absolutely have to put everything into making it work.
Cena's capabilities to manage the role shouldn't come into question, he knows how to work the crowd, and he's certainly shown glimpses of heel-ish behavior in specific matches. The key example that comes immediately to mind would be the One Night Stand match with RVD, with him both treated as a heel and acting like a heel, and intentionally trolling the crowd, which also happened to be the night that fully sold me on Cena's ability to work a crowd, yes he'd done it many times before both as a heel/face, but that night he showed he was more than capable in the situation.
It's tough to really say how a heel Cena would do in today's enviroment. He worked as a rapper, because he had more free reign to work with. A lot of what helped get Cena over was the edginess of the character. He could be a total bastard, he could insult people in the most amusing of ways and people liked it and got behind it, he was "cool".
Could that gimmick work today? Well, possibly, I think in today's environment he would be restricted though.
That being said, I'm not holding my breath on it happening, Cena is still the de facto WWE babyface, Reign's at the moment doesn't have the backing to be in that kind of position.
In all honesty, keep them far away from one another.
Even pitting them face vs. face, wouldn't work. The crowd currently aren't behind Reign's, and most of the crowds wouldn't be behind Cena, especially if Cena was going for another run with the WWE title. Reign's needs to be booked more smoothly into either a face role of heel role, though I believe that at the moment, WWE might have booked Reign's into a corner.
Turning Reign's heel at the moment would be the best approach to take, build him up again, then turn him face once more. Let him get over as a heel, and if you allow him to do what he has the build to do, the crowd will get behind him, then you turn him later down the line, even if it doesn't work and he doesn't catch on as a face, you'll still have a monster heel to work with.