One of the places I take off is in a place where it takes a few minutes to acquire sattelites. I was going to take advantage of that time to callibrate my compass, however I got to wondering if I should wait for sattelites first. Does the calibration use the sattelites?

Compass calibration should only be done once, not before every flight. Unless you travel a couple of hundred miles from the last good calibration point.

Doing that over and over, you run the risk of a bad compass calibration, which will be a bad thing.

Some of us like to recalibrate the compass after doing a firmware update, or when a new Go app is installed. Other than those rare occasions, leave it alone.

Calibrations don't wear off, or disappear, when you power down.
No, the GPS and compass are two different aspects of your drone.

RedHotPoker

Go back to your manual and read what it says at the top of P57 to find out what you should be doing about compass calibration.
To answer your other question:
The compass is there to detect the earth's magnetic field and allow your Phantom to fly straight.
GPS is receiving signal from satellites in space to provide position info.
These are two separate systems and not related.