Ok it can work. Pressure is not relative. Hence why bonnet scoops work better facing the windscreen than the front of a car. It's also why your air conditioner draws its air from the same low pressure area at the front of the windscreen and not the grill. You will also have a massive problem with condensation on the inside of the windscreen in cold weather. Most car ventilation systems draw air from outside when on the defogger setting. Never on recirculate.
I think the under dash vintage air is a good way around the problem. You need to think about draining the condensation that forms on the receiver drier though. It will rust the floor pans out the way it is.