I'm in FL, so I know....
Yes, the a/c drys the air. W/o the compressor running, you are just blowing the same humid air around. With my old VW, the only way to defrost was a hand towel. No amount of fan did anything - when its 100% humidity both in and out of the car.
As an aside, this is one reason you "size" the a/c in your house to the size of the house. If the a/c unit is too big, it cools too fast w/o removing enough humidity from the home. Plus, the humidity makes it feel hotter than actual temp (so you turn it down lower), while dryer air will feel cooler in summer.
Lots of the new super-efficient home systems have a dehumidifier/air dryer separate from the ac compressor, so the chilling can be different from the humidity level.
Edit "defrost" should be changed to "de-FOG." But its probably the same with frost - its just frozen water.