No, Newt was a big Dole backer in GA in 1996; I specifically remember he was. Dole did not see fit to return the favor.
When Newt ticked off Dole was in the ‘80s. He called him the “tax collector for the welfare state” and he got language changed in the party platform to make sure tax hikes were not on the table as Dole wanted. Obviously they were allies when they were the House and Senate leaders in the ‘90s, for pragmatic reasons. Dole also offered to loan Newt the $300,000 to settle the ethics attacks by Democrats. Newt fought the party over the platform but when it comes time to vote he does not undermine the party’s candidates. I’m pretty sure that’s not a rule you can really break if you want to stay in the party.