Yes, why not. I think at the heart of the matter though is whether you could imagine a Rose Tyler companion going through training and taking to wearing a Batwoman/Wonder Woman style costume?
In the original series it would be absurd, that isn't the world Doctor Who operated in. But the modern series rapidly demonstrated it has no internal or storytelling rules it is governed by, instead anything goes. So when Russell Davies introduces Jack Harkness he is almost a spoof, then Davies gives him immortality and he is effectively Captain Scarlet, a Superhero, wearing a trenchcoat and dashingly handsome. We see UNIT has its own Helicarrier. The Master is reintroduced and he too is super-powered, a cackling Marvel Supervillain capable of shooting energy and flying through the air. We have those unbelievable Monks in 'Tooth and Claw' who are clearly only one short step away from superhero territory. You can look to Madame Vastra and Jenny as a superhero couple, Bill Potts ends up as a cosmic powered being, The Doctor himself can now take hitting the ground at a hundred or more miles an hour from a great height and get up, He can take multiple hits from Cyberman weapons and a ground zero nuclear scale explosion completely unscathed as the environment around him is obliterated.
So is it reasonable to propose the character today, and his/her/its world, is in fact already a Superhero one - that the Doctor has been refocused as a Superhero? In the original series it would be absurd to have Ace or Peri in any sort of a superhero costume - that wasn't the world the show and its characters operated in. Today, you could do that, you could do anything, and that is not a good place to be for the show I feel. Even Harry Potter's world is governed by rules and the storytelling dictated by its many limitations, Doctor Who on the other hand isn't governed by anything at all as far as I can see... it's all been washed away over the course of fifteen years. Anything goes.
The Drwent from being the james Bond of outer space to now being more akin to a Dr Doom wannbe!