I could , but not by enough to matter if your head is working. The one time I had a "bad" location from a GPS was in a canyon. I was in a rock shelter on the east side of the canyon, and the GPS put me in the bottom of the same canyon, but in the general area.

Compasses can be affected by local magnetism (many different types, like ore bodies). None of these affect the constellations and Polaris, except clouds. Be aware of your surroundings and examine all your available tools.