The GPS signal is still there, as the satellites are in orbits at about 21,000 km, far higher than the ISS.
Software the limitations on speed and velocity within the receiver would stop them from working, but this is a political not technical issue.
As a technical issue, the added Doppler from being in orbit would cause the GPS receiver to fail to acquire and track satellites correctly - a ground based receiver is only designed for only +/- 5kHz of Doppler shift away from the nominal frequency. This not only affects the tracking loops within the receiver, but also the bandwidth requirements of filters and antennas.