As we all know...warm air rises. And so does warm moist air, to a point. In addition the "draw" of the vent will transfer the air to the outside but here's the problem. For the exhaust to work properly it will need some make-up air from some place. It won't be coming from the shower, so any moist air that gets relocated to the outside will be because it has simply fallen in line with the other air in the room and any air that is being drawn from under the door or through a floor heat vent if there is one.
Typically those bathroom exhaust fans don't work that well. If yours has the volume ability to move air to the outside it may work for you but I doubt it.
I would put the exhaust fan on a timer so that it can run for a couple of hours after the shower is used.
As far as the gap above the door, the eight inches represents about three square feet of air space. The power of the draw of the exhaust fan will determine how many cubic feet of air (times three) can actually be evacuated from the shower area in a given period of time.
Maybe changing the fan should be considered.