Possibly. It all depends on the quality of the installer. The mortar is supposed to be struck (removed) from the inside. Key word: supposed. Normally what happens is that as the mortar is struck from the cavity side, a lot of it falls to the bottom. Or, if too much mortar is used, it squeezes out and just falls on it own. Either way, it blocks the bottom. The mesh is supposed to prevent the mortar from plugging the weep holes.
There is only one way to find out - drill in from the bottom and see if you can fish up. If so, it should work.
Hmm. I have a lot of experience with fishing wires and I'd try your first thought before trying the second one. If it was a hollow, empty wall, then OK, but full of insulation = difficult - unless you're really good.
What is inside the building directly opposite where you want to penetrate the brick? If it was in a closet you could run the wire down the wall inside the closet and drill through the floor.
If it's in an open room and a blank wall plate was acceptable you could drill through the brick into the room, drill the sole plate, and then put a blank plate on the wall - or use it as an excuse to add an outlet.
It depends how close you are to the brick ledge, which is outside. It could be 3' below the structural panel, or it could be right at it. I have seen houses where the ground is higher than the structural panel. I would drill the structural panel and see if you hit mesh or not. The mesh should be plastic, no big deal, it is only used during construction to keep the wet mortar from plugging weep holes. If it seems clear, try fishing. If not, try your second option. As @Moonville says, fishing through insulation is frustrating. The cavity should be open. Brick ties are only an inch or so wide, spaced at 12" or more.