No he wouldn't because Neelix was in Love with Kathryn and he was doing his best to hide it.
Neelix says stuff in Deathwish and Ethan backs it up in an interview.
But the kitchenrat beleives that he is not good enough for her so there's no need to get rejected and then be asked to leave the ship because he's making her uncomfortable.
Neelix is twofaced a liar enough to hold all this in as secret.
It's the Tuvok half that wants to be honest and exploding the world around him.