Why would Cat doubt that was Kara? She is just some average person with no special insight that would give her the ability to detect any deception. She can be fooled just as easily as anyone else.
Didn't at all mean she would doubt it was Kara. She would be fooled, of course. But fake Kara was so awfully out-of-tune with Kara's real self I couldn't stop thinking of how that all sounded in Cat's head. It must have been bizarre. He didn't just stumble, he was basically all over the place. So off I don't know why they didn't all the way with Melissa Benoist imitating David Harewood a little (not as far as Anna Torv doing a full impersonation of Leonard Nimoy, but something in that direction).