Do Induction Motors only work if the rotor's coils have a finite resistance?
Superconductors are impervious to magnetic fields, so if you have a superconducting rotor no fields lines will enter it. (or pass through the apertures of the squirrel cage)
With no field lines in the rotor there will be no torque.
you could possibly get it running synchrounosly as a variable reluctance motor. but you'd need a way to start it, and there wouldn't be much torque available to keep it running.