Fizzle, most likely, but still. The (not-so) old half-second heal reaction would have to disappear, or battles would end at the whim of random numbers. Well, more so. Strategies and tactics would have to arise, to take the place of reflexes.
Well this would solve many of the problems WoW is having with bosses having to hit ridonkulously hard to be a threat, as healers heal for too much. If they aren’t guaranteed to actually heal for silly amounts, the bosses don’t have to hit as hard.
Bonus fun: if the tank’s avoidance against boss hits makes the heals less likely to land.
Now I’m oddly reminded of Final Fantasy Tactics and their “Faith” mechanic. Characters had a Faith value, which affected how strongly magic worked on that character. A character with very low faith would be almost completely immune to magic… both damaging and healing.
I know, it’s not the same, but it still made for some interesting choices when it came time to field a team for a fight.