If the box is rigidly mounted, you could get the necessary friction force. I think it works like the Kepler Commuter Booster. Once it gives power, the friction drags it further round to give a servo effect, and when you free-wheel, the direction of the wheel pushes it back out. The Kepler one is very simple and clever. It totally disengages during free-wheeling, and uses the motor torque to bring it back in contact and then self-servo into full drive position.
it looks like a lot of development has gone into this one, so I'd be surprised if it doesn't do what's claimed, especially as the claims seem conservative and realistic: 18 mph and 12 miles.
I guess you need the right tyres for it to work properly, especially in the rain.