|Ummmmmm ... not exactly.|
Still, it's missing a crucial element: to be a religion, the fanbase would have to do everything they're doing, plus make the assertion that there is a Time Lord out there with a TARDIS doing all the stuff the show describes. Without that assertion that the fantasy describes something real, I don't see how how you can make the case. Religions all pretend they describe reality in some way. As far as I know, neither the show's creators, nor the fans, have such any such foolish delusions.