Cellular data will not help the compass, but it might help GPS get a quicker fix. Android's high accuracy mode uses wifi and cellular data to help determine location and speed up GPS aquistion process. The GPS fix should be the most accurate, but may take a small bit to aquire Check out Google Maps whenever you have issue and see if it has an accurate fix of where you are and direction you are headed. Otherwise, makes sure the setting really are the same (check the accuracy of Location Services, make sure the apps have access, calibrate the compass, etc)
Plenty of devices work without cellular data, so it is not a requirement.