I believe their approval rating DOES affect how they play. But in the case of rookies I don't think kicking them out of negotiations a few times affects it.
I have noticed that with veterans who want a new deal, if I am ignoring them their performance will drop and their approval of me will as well.
I always sign my rookies to offer #1 until they come up with their "This is it or I walk" which happens every now and then. Otherwise, they get #1 deal with it. They always sign before game 2, I can even get some free approval points by waiting till after season goals come out to sign them. Get a Free "Sign so-and-so" approval bump.