I don't know how the [strike]freewheel[/strike] cluster thing attaches, but if it simply threads on like a freewheel, backpedal forces will eventually (if not immediately) spin the thing right off.

And if you're thinking of a multispeed derailleur-shifted fixed gear bike, don't do it. Any time you're applying any backward pressure at all on a fixed drivetrain, you're pulling the bottom run of the chain taut. Imagine what that's going to do to the poor rear derailleur...