IMO, there are some production realities that would have to be accounted for. Not the least of which is that Jodie is not overly tall statured and if her replacement is male (or otherwise taller - Jodie is 5'4" sans footwear and all the other modern Doctors have been in the six foot range), odds are they'd look more than unusually awkward running around in her old clothes before finding a replacement kit. Not impossible by any means, but knowing RTD I'd not be at all surprised if he started his return with the new Doctor in medias res, leaving only visual clues and a verbal reference to being shorter and blonde when they last looked in the mirror.
Mark