Well, no, because then photons would have infinite mass, but they don't.
And if theorized faster-than-light particles called tachyons exist, why haven't we ever detected Cerenkov radiation in a vacuum?
Because tachyons do not have an electromagnetic charge. Similarly, many neutrinos pass through the air in your room every second at a speed faster than the local speed of light, yet they do no emit Cerenkov radiation.