Prot paladins get a ton of tools they need in the lower half of their tree, including large boosts to stamina, damage reduction and block. You won't get near any of them with a holy build.

In PvP, agro isn't an issue, you'd just be a healer.

In PvE, I don't know that there's any way to generate more agro through healing than DPS. It may be possible with a ton of micromangement and coordination of Hand of Reckoning, Hand of Salvation and Soulshatter.

In PvE, gear is never going to be on your side. Defense/melee gear has no spell power, crit, int, spell haste. Healer gear has no defense, low stamina, no block/dodge/parry. Blizz has gone a long way down the nerf road to make sure of that. You would need to count on PvP gear with resiliance to get you crit immune. You would need substantial amounts of haste to spamheal your way out of incoming damage, even with pushback resistance. Also, you get 0 block and parry while casting, which you will be doing 99% of the time.

It may be possible, just about anything is with enough {fill in the blank}, but I see it being a lot of work and a lot of reliance on luck and gimmicks at the end of the day.