Can you pair a compass or magnetometer with an induction circuit to create a form of metal detector?
Yes, it is quite commonly done, sometimes even with large sources/detectors operating at 100km/h or more ~100m or so above the ground. 

The ground is more-or-less conductive so you also see the fields from currents induced in the earth. And any other nearby metal as well. 

Secondary and primary fields can be distinguished by phase. ahem the devil is definitely in the details.