VoxFox, I'd be more worried about the heat than the motion. Heck, the sneakers get tossed about in the washing machine anyway, and for years a trick to help keep items fluffed in the dryer (blankets, sleeping bags, heavy towels, etc.) is to toss in a sneaker to act as an agitator. But between the rubber soles, the canvas uppers, and the foam insole, I'd fear that dryer heat could damage the shoes.
My thought was to put them in the dryer, with some other heavy items, and run it on the air-dry setting--no heat.