It probably "could" be done... but you "can" drive a screw with a hammer.
What downside is there to using a simple rotary encoder, if you mean by that what I mean by it? (A simple little thing that gives you ons and offs when the object rotates) With two of them, knowing which way the wheel is turning is a doddle.
If you go the motor route, be sure to include a diode to clamp voltage spikes.http://www.arunet.co.uk/tkboyd/ec/ec1relay.htm
Yes.. that tutorial is about clamping voltage spikes from relay coils. What you are talking about will create the same spikes.