Do it! You'll clay your car faster than you ever believed possible!
I actually just store it with the clay facing up totally open. I just lay it flat so that nothing is sticking to any other part. I can see how it would stick to itself though...
As far as dust getting onto the towel while in storage, I try to rinse or wash the towel before I use it on the paint.
I'm just worried putting it in the garage like that. My dad likes to have the garage door open all the time and crap always manages to fly in there.