Yes, a coaster brake rear wheel will work as long as the wheels fit. You may need to respace your coaster hub though, which is not a big deal. A 700c with skinny tires might fit the mountain bike - if a 700c wheel fits in the frame, you will be fine, though I don't think you'd have much tire clearance. I'm having a hard time picturing it, and I don't have any 26" mountain bikes to try it on.

Are you going to be running front brakes, or just the coasters in the back?