Well i never heard any of such sound in my vehicle. But despite of that, if you open the fan of your car with some screwdriver, and you trace down the links, you'll get to know that it has no connection with compressor at all. Instead it's just a blower who has a fan attached to a motor, and is throwing air comming out of compressor outlet. That's it.
Psychologically it really has a link to car's performance, whereas practically and electrically it works independently. That's the only reason you can even use it on your 12V battery.