Your question is a little confusing. Turning the A/C off doesn't turn the climate control fan off...there will still be air moving through the vents just not air-conditioned air. Unless you turn the climate control system completely off (which you normally would never do) there will be some air moving through the vents, closing the dash vents will shunt all that moving air to the floor or defrosting vents.
Not sure why you would ever turn the A/C off in this car anyways...it's an integral part of the HVAC system even in the winter. Don't turn the A/C off. A tightly sealed box with people sitting in it needs A/C in order to maintain a comfortable environment regardless of the outside temperature.
The interior temperature of the car will be maintained at the temperature you set using the two dials on the dash. These dials do not however directly control the temperature of the air coming out of the dash vents. This is controlled by the red to blue dial below the center dash vents, red being warmer air and blue cooler. This is a BMW system and is initially confusing to new owners but it allows you to keep the car at say 72 degrees but have cooler 65 degree air blowing on your face. It makes more sense if you are German I guess.