It's do-able.

My fixed gear conversion started life as a Raleigh Technium mountain bike. I laced up a set of 700c rims onto Surley hubs. The reflector hole in the (rigid) front fork turned out to be perfectly spaced for a normal reach 105 brake caliper. Since my bike is fixed gear, I don't use a rear brake.

I suspect you'll have rear spacing issues. Most mountain bikes have 135mm rear dropout spacing and most coaster brake hubs are 110mm. That's a whole inch of difference. Assuming your frames are aluminum I don't think you'll be successful in respacing them. You may run out of axle length if you try to respace the hub and you'll have to do something with the coaster brake torque arm.

Good luck.