I was gonna seal the gap between my garage wall and the fireplace with some
of that "Great Stuff" until I can afford the time to do a proper fix. My
question, would having this foam on the OUTSIDE of the fireplace (i.e, the
part of the fireplace that isn't exposed to fire and is in fact not even on
the same side of the wall as the hearth) constitute a fire hazard?

The gap is immense and the drywall needs to be replaced as there is quite a
bit of water damage.

If there are other options, what would they be. I estimate the gap to be
roughly triangular, about 4 inches wide at the base.