No, Kate never invites Nico in for "hot coffee". Ironically, she seems to be the only one of the "girlfriends" in the game that he actually likes (and me too, if Kiki's special ability wasn't so valuable, I would have kicked her to the curb long ago).
Dating Kate isn't a waste of time though, she is a pretty important character as the game progresses. I don't know what would happen if you tried to dump her, but I doubt it'll let you.
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