I doubt this will see play, even if odd priest becomes a thing.

Historically speaking, cards which are dependent on having a bunch of other minions have been pretty lackluster. In fact, I can't really think of a single card that depends on having a big board that sees play at all. The closest I can think of was Reliquary Seeker which was sometimes included in zoolock decks, and there your worst case scenario was that you got a 1/1 for 1 mana - shitty value, but not really that much worse than most other 1 drops.

This card is outstanding if I have 6 big minions on board, but if I have 6 big minions on the board I'm probably already winning and don't really need the boost. Conversely, if my opponent isn't letting me keep anything down then this card is a weaker Yeti that I'm paying 1 mana more for. Essentially, it's strongest when I don't really need a strong card, and weakest when I need a strong card the most.

On top of that, I don't think that this card really "works" with priest. Health buffing is certainly a priest thing, but it's generally done by buffing up a single minion to hit with Inner Fire. Since Inner Fire only affects one minion, buffing my other minions isn't really helpful - and I'm paying 3 mana more than I would for a Divine Spirit which would do the job just as well.

Only way I see this card seeing any play at all is if odd priest turns out to be a ridiculously strong deck with a desperate need for a Divine Spirit replacement but also is okay with a massive mana cost which makes it impossible to combo it with a bunch of other health buffs. Given how improbable that is, I'm pretty confident that this card is dust.