I dont know enough to say that about his "entire franchise", but if the only feat of this Star is that it makes him invincible to his gameplay enemies within the gameplay then its useless to him in this fight.
Also I have seen cutscenes, probably from Mario galaxy or sunshine so I am quite sure theres canon text or storyline that bases a lot of what Mario can do. Probably wont help your case for the Starman though.
Whats your claim? that because of the gameplay mechanics around the Starman making him immune to mushrooms and what not, he can survive against any fictional attack from any universe simply because "his invincible with a Starman!"?