Totally. I'm nitpicking, but it really is a missed opportunity that they didn't just give him a different title like the Warrior, Exile, Renegade, Colonel, etc, etc. It would've reinforced how he was something different (at least in his own opinion of himself) and made it more of a big deal when he earned the title of the Doctor again from 11 & 10 (and yes... it would've neatly sidestepped the whole "messed up numbering" aspect, which I know some fans care about, though I couldn't give a hoot in Hell about it).
It'd also be a subtle nod to the possibility that there might only be 12 (acknowledged) Doctors, but other incarnations of the same being who didn't call himself (or herself) that. Whether or not people buy into "The Other", we know the Valeyard's still on the way...