I doubt this trade will have any effect on Hayward staying or going. Hayward is a smart guy. Sure he wants the Jazz to make every effort to retain Hill, but he knows that having 70% of the salary cap tied up in himself, Gobert, and Hill is not winning combination. This is good move whether or not Hill stays and, honestly, whether or not Hayward stays.
If Hayward leaves, it's simply because he wants to go. Hopefully that's not the case. While everyone in the media has something to say about it, the man himself has said very little.
Hopefully, he knows that the team 1) is trying to retain Hill for a reasonable salary, and 2) is trying to improve at PG. If that's not enough, it's probably an excuse and he wanted to leave regardless.