Our house has a large double sided fireplace right in the middle of it. It has a vent above the doors on either side to circulate the hot air, which is not all that effective. I wondered if it would help to have air forced across the firebox and decided to try an experiment. I rigged up a window fan to blow air into the vent in one room.
It actually does help. It makes the living room, on the other side, nice and toasty.
The average fireplace is probably only about 10 - 15% efficient. That’s before you factor in the impact of the draft on the conditioned air space in your home. Ours fireplace draws extremely well. If we ran it with the doors open it would suck the air out of the house faster than it could heat it. Fortunately it has a fresh air intake from outside but which helps minimize the air drawn from the living space.