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I would say that Yes it does. Combat is still combat. Even if it's from a different room.
Blossom hasn't been used in any of my games yet, but I'd probably play it how Trueflight suggested, as Blossom's ability doesn't mention combat, only that "Your <bow symbols> can hit an adjacent room. If a Monster is defeated that way, no Treasure Card is gained."
It would then mean every Monster's start of combat ability would have to be ignored if Blossom attacked them from an adjacent room, which makes sense if playing it this way. (It could be said that thematically she's acting as a sniper from afar).
Plus any monsters with the Quick Stab ability would also have to be ignored. I guess her ability is mitigated in that she doesn't earn a Treasure Card from these types of sniper attacks.