The trigger still has to be pulled for each shot, and each pull only fires one shot, so it is not true automatic fire. It would be no different than rigging up a hand crank with a cam to trip the trigger with each turn of the crank. At a gun show I saw a pair of Ruger 10/22 actions rigged this way to make a sort of Gatling gun.
In the videos I've seen of these devices, the gun has to be held very loosely to allow the necessary back and forth movement. Partly or mostly because of this, it was also striking that although a lot of bullets spat out in a hurry, they did little more than kick up dirt around the target, with few rounds actually hitting it.