From a strict 3 boxing PvP perspective, healing is nice but can be had in ways other than simply casting heals. Aka shadow priests, warlocks drains, shammys, etc. I would still consider SOME healing no matter what.

My experience with 3 boxing is limited, as I went from 1 boxing to 5, but healing is something you will still want to think about. I assume one would do battlegrounds AND arenas - so healing will still be important - otherwise you will have to either let them all die when one dies, rez one of them (implying healing ability) or run back to their spawn point. None of which are as sexy as staying alive in the first place.

Perhaps 2x shadow priests 1x holy? Or 3x shadow with the ability to morph one out of shadowform to heal? Or 3 shammys?

Personally, I would never consider a 3 box that had NO healing unless there was a very specific reason to do so - which would preclude versatility in other situations.