Hell yes Troy would cosplay as the Doctor! He's already cosplayed as robots in canon, at least twice that I can think of. Troy ♥ (I for one am glad that March Madness brought out the Troy love, because he's awesome and it's nice to see a smaller fandom get some attention.)

...Now I'm going to be singing "na-na-na-na-na-na-na-na-na-na Katamari Damacy" all night, and get weird looks. WORTH IT.