Fixed gear / flip-flop wheel on a bike with a freewheel crank (schwinn caliente)
 

Just out of curiosity, would a schwinn bike with a freewheel crank (crank has the freewheel) work just like a normal single speed? Or did the original backwheels also have a freewheel? Would there be any disadvantages to running this way?

Thinking of getting a towny in our garage up and running.

The original rear wheels had a "friction freewheel", it would usually not move but would slip in case the chain jammed up. You could run with a fixed cog or with a freewheel. If fixed you have the usual concern about getting your shoelaces and pant cuffs ripped off and crashing if you aren't careful about what goes near the chain.

I had a Ross 10sp (Eurosport?) with FFS (front freewheel system). A couple things come to mind:
On the freewheel side in back, there might be a noticeable / annoying amount of slack to take up after gliding to engage both freewheels.
On the fixed side, you have the risk of catching something on the chain, possibly complicated by the fact that your feet might not (initially) be moving in sync with the chainring.