Whoever said that cranking to gimbals and supporting the missile will make your shot more accurate probably meant that it is more accurate than shooting and turning away without supporting the missile at all. As you said, it allows you to support your missile while reducing the closure rate, making the bad guy's shot take longer to get to you.
Some other things I do after cranking:
If I know or think he has a shot on me, I will often break off and run defensive 5-10 seconds before I reach pitbull, but only if there are no friendlies between me and him. If your target does not do any radical jinking, 9 time out of 10 your shot will still find him. And as you have turned away early, it is easier to defeat his shot. Better to save your plane and have the ability to set up for a 2nd shot than try and support all the way to pitbull and potentially eat one yourself.
If I am planning on breaking away before pitbull, I go to STT (hard lock the target) a few seconds before turning. Sometimes this spooks them into turning their jammer on, giving you a HOJ shot.