Nail plates are only required if the hole drilled through the stud is closer than 1 1/4" from the face of the stud. So if it's a hole for one wire and it's centered on the stud, there won't be a plate.

Assuming there's no plate, a screw that is shorter than 1 3/4" won't hit the wire, but in this case OP is talking about a wall mount which likely has longer hardware. You'd be very unlucky to catch a wire, but it's not impossible.