"Yeah, who the hell are you and where is the *real* Doctor?"
Oh hell, yes, totally! Somebody should write a fic about Rose meeting Morrissey!Doctor. That would be made of win!
And yes, you're right. He's just as River described "her" Doctor. Arrogant, snapping his fingers at the tardis... then, Ten did try at the end of the episode... And I sooo wanted Donna to slap him because of it.