Yes, but I suspect that is a function of geometry. For example, it is possible to have a lighthouse whose beacon is spinning so quickly that the spot of light in the distance (at some distance "r") is moving faster than c, even though the rotation of the lamp is not faster than c, nor is the actual light beam. - 1pg

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That makes for an interesting thought experiment. As the lighthouse beams radius approaches the point where the "tip" of the light beam approaches the speed of light, what would it look like if you could observe it? Perhaps better to visualize some distant wall against which the light beam sweeps. Rather than extending r to some humongous distance, you just keep accelerating the rotation of the beacon.

At slower speeds, the beam traces a continuous path across the wall. This is what we experience in everyday life. But as the sweep speed reaches and exceeds c, it seems to me the sweep would not be continuous but rather become a series of spots separated first by the planck length, then as speeds continue to increase past c, the separation of the spots would increase I suppose all the way to infinity.

The size the "spot" seems like it would have to shrink ultimately to the diameter of a single photon, if a photon can even be said to possess such an attribute. Perhaps it is better described as the beam disappearing altogether but then do you still have a beam at all after c is reached?