romex - drywall over plywood
Well, if it was an addition then the plywood was the old exterior sheathing. There would have been no reason to remove it. It is absolutely typical to leave it in place.

If you are simply putting a new receptacle back to back I am not sure why you think you need to remove wall material to go through studs.
If you are implying that you need to go laterally along the wall to get to the new box location than NO, the cable CANNOT go along the surface, or even just below the drywall. You will in that case need to cut a channel in the wall to drill and cross studs. This can be done from either side if you don't want to mess with the plywood.

If you have the wire already through a hole you just need to cut a box into the drywall/plywood. A jig saw, RotoZip, MultiMaster, etc, will do a fine job of making the hole for the box.