I hope that you're talking about an electric clothes dryer! I don't think venting a gas (either natural or propane) clothes dryer in an enclosed space would be such a good idea. Carbon monoxide anyone?
Yes, the gas burns clean, but even most if not all garage box heaters (Hot Dawg etc.) have the combustion gasses vented outside, do they not?
I may be wrong, but that would be the main reason not to do this, aside from being very inefficient. Just my take....