My son carried his backless TB as a carry-on, and it fit in every overhead compartment we encountered, even the small ones. The smallest overhead compartment we encountered required a bit of wiggling, but once it was in it was fine. I think you could easily get the back into a carry-on with wheels, but then of course you'd have two carry-ons instead of just one. I'm not sure you could fit both the base and the back into a carry-on, considering the height.
I think your best bet would be to carry the base, then pack the back into a bag however it will fit, and hopefully have some room to pack his other carry-on items around the back.
Oh, and if you do end up carrying the base separately, you might want to get a strap of some sort for it. We took a FPSV booster and a TB, and I found the FPSV was much easier to carry because it had the belt-positioner strap on it. I tied that strap to the seat and had a "handle."