Like others have said, as long as the rim fits on the bike, it should work.
You may have to build the wheels, though. There aren't many options for pre-made 700c rims laced to coaster hubs.
The other thing to think about is chain tension. You can't use a mechanical tensioner with coaster brakes, so you'll need either a magic gear or horizontal dropouts.
Did you mess up both hands? Not to belabor the point, but a front brake would be a good idea if you're going down any kind of hill and/or wet pavement with skinny high pressure tires. You could use a drum brake front wheel like I have on my coaster brake Steamroller. No problems with reach or mounting points.
Originally Posted by
JohnDThompson
It will work, but keep in mind a single rear hub brake is not a very effective means of stopping a bicycle. There's a reason why you only find coaster brakes on children's bikes and low-end department store bikes that are unlikely to be ridden fast or often.
They're on a lot more bikes than that. Aside from overheating from heavy use they work just fine. Like all rear brakes, they are safer when paired with a front brake.