I will add something
The Washington state cpl does away with the state requirement for a waiting period (5 business days IIRC), but has no effect on any corporate policy. IF the store has a waiting period policy, (and some used to, although most of them have gotten out of the handgun business since then) you will have to wait.
All Fed rules apply, as well as any state paperwork needed. Only the state waiting period is waived by the cpl