Strictly speaking, I'm struggling to think of an MMO healer that specifically gets damage back from healing without resorting to sort_of_ism's by way of time/opportunity as is the case with Warrior Priest.
I have a nagging feeling that SWTOR might have had something close but I'm struggling to put my finger on it, Combat Medic had a filler heal that generated their ammo resource but I'm struggling to remember if any actual damage was gated behind it.
Another of Warhammer Online's healers was a mage that theoretically had to evenly deal damage and healing output to balance a gauge for optimal potencies but from memory it was a bit of a bust and to my memory at least, never really quite worked as intended. WOL's cleric type healer was built around a buff/debuff rune gimmick rather than direct damage.
Beyond those reaches and of course, FFXIV WHM I'm at a bit of a loss.