This is also quite chilling.
Or course The Doctor exists in a universe where there is no Doctor Who-based entertainment. Now that I think of it, being that this is the only universe we know to exist, this seems pretty unlikely. Has he ever shown up and had the TARDIS swarmed with fans?
episode idea: He finally repairs that circuit that allows the TARDIS to change shape in order to blend in, and then his next hop lands him at an SF convention where it turns back into a police call box and freezes.