I'd say "no" according to my belabored definition above. But enough about that.

My daughter has one of these, an old Schwinn Caliente with a Shimano Positron II drive chain that we rescued from a dumpster.
You are correct. The back wheel is fixed -- even though there are 5 gear wheels on it for multiple speeds, it is rigidly attached to the wheel and the gears won't move relative to it. That's to force all the free wheel movement to the bottom bracket.

The advantage of this design is that you could change gears while coasting because the chain continues to move. I always wondered, though, what happened if your pants cuff got caught.