I have a bike like this, it's an old Schwinn World Sport, and I took off the shifters, deraileurs, shortened the chain, etc. Here in Prov we call that a "Hobo" SS. It works but like Mouton said, watch the chain tension. Like with my setup I can either have it in my highest or lowest on the bike, nothing in between, because of the ammount of chain that is available without using my chain-tool.

All in all that bike should work, just keep an eye on tension and alignment and you should be good to go.