Not correct. With or without a CCW permit you take possession of the weapon upon purchase. You still have to fill out a 4473 but the FFL just doesn't have to phone it in, which saves you time and the FFL work.
The only benefits to having a permit that I can think of are interstate reciprocity and the fact that you can carry in an establishment that serves alchahol - if you're not drinking
We should also add that the AZ CCP gives you reciprocity with about 32 states, allows you to carry when a Federal statute requires same in specific circumstances (1000 ft of a school) when State Law is silent.
Likewise, it identifies you to Law Enforcement as to being a legal possessor at time of issue.