if the AC does not work at all , there will be other issues .
if it does not work whilst the car is stationary , the fan will be the problem , so the AC should still work when the car is moving due to airflow through the condenser .
I don`t think the fan controls the compressor in any way .
there was a very good thread recently on AC issues so try the search function at the top of the page and see what you find .