I wouldn't! While the fact that you have a fan in the exhaust indicates a high efficiency furnace and the temperature is thus low enough it probably wouldn't ignite dried paint, I still wouldn't chance it.
I find that a filtered booth cuts down a lot on the fumes. The filter collects the paint particles and they seem to outgas more slowly when stuck on the filter than they do in the air. Probably less surface area. I see two purposes for a spray booth- cutting overspray in room, and reducing fumes/smell. The filtered booth with no outside vent certainly fulfills the first purpose, and does help some with the second.