I'm not sure how boxing-friendly a priest is, but I do know a Discipline Priest can be a very nasty opponent in pvp/arena. They're hard to kill and have several useful abilities like Pain Suppression, Power Infusion and Divine Aegis.

If you're going pvp, I'd go deep Discipline or deep Shadow, but not focus so much on the Holy. It is better heals, but more of a PvE focus while the other two trees are more suited to pvp's. I'm not saying it won't work, but if you want a priest healer build, deep discipline will likely serve you better.

I'm just not sure how boxing friendly it is. For heals, Pain Suppression and PW: Shield, you can assist your dps toon and "/cast [help] Spellname; [help, target=target] Spellname" or just have the ability hit your priest automatically if you think they'll focus the healer. "/cast [target=player] Spellname".