Other replies in this thread show that some specialized datums do depend on the earth's magnetic field. However, geodetic datums are determined ultimately by the earth's gravitational field, which establishes the "geoid" (an idealized "sea level," or contour shell of gravitational equipotential). The geoid is then approximated by an ellipsoid of revolution that is coaxial with the earth's axis of rotation and concentric with the earth's center of mass. The geoid is known to within a few centimeters and its ellipsoidal approximation is good everywhere to a few meters accuracy (and never worse than about 100 meters). (In contrast, the ellipsoid itself departs from a spherical model of the earth's surface by up to 23,000 meters in places.)
Because the net magnetic charge on the earth is extremely close to zero, any changes in the field will not measurably disturb the distribution of the earth's mass. The influence is actually in the other direction: electrical currents in the earth's outer core, the "geodynamo," are believed to create its magnetic field. Mass flow within the core can therefore change the magnetic field over time, including the direction of its dipole moment. It is possible that such movements in the core may, very slightly, change the earth's center of mass and thereby perturb the ellipsoid. I suspect that such movements are so slow and inconsequential that these effects cannot even be measured.