Giving Hayward that extra money will only hinder their efforts to put quality players around him and pay them.
If I was Ainge, I wouldn't go after Hayward anyway. I'd try to entice Chicago to give up Butler for the #1 pick. Butler is as good or better than Hayward and is signed to a very reasonable contract for the next 3 yrs. Then, I'd use cap space to sign a PF like Ibaka or Milsap. A lineup of Thomas, Bradley, Butler, Ibaka, and Horford with their bench would be pretty sweet.