Is it possible to put a chain on without removing the rear wheel? I have a bike with a single chainring up front and an internal hub and a coaster brake in the rear. (For those unfamiliar with this setup, it's essentially like having a single-speed bike in that the chain is exactly as long as need be, and tension on the chain is adjusted by moving the rear wheel in the rear dropouts before tightening it.) 

My preferred procedure for cleaning the drivetrain is to completely remove the chain. The obvious way to do this would be to loosen the rear wheel in the rear fork and take the chain off. (Remember, no rear deraileur and no chain tensioner.) However, rear wheel placement with an internal hub can be tricky. 

If I were to install a chain with a master link,  would I be able to remove the chain without loosening the rear wheel, or would the tension on the chain make this operation difficult?
It depends on the style of master link and how much chain tension is in your setup.  An SRAM power link needs about 1-2mm of chain slack to unhook the link.  If you can find this amount of slack, it should work with most types of master link.  If your chain doesn't have 2mm of play, but isn't too tight, a master link that snaps off the side (like the first one pictured in the terminology index) should work.

The tighter your chain, the harder this is going to be to snap back together.  Depends if you would prefer fiddling with a master link on a tight chain versus the re-aligning the rear hub.