CPL status does pop up if an LEO runs your info iirc.
Depends on the agency, but the default is no... A normal ACCESS return does not include CPL status, it includes NCIC/WACIC and Drivers Status/DOL. CPL is run separately, but some systems are designed to grab the required info and run a CPL automatically. Also, a CPL only shows when being run through DOL database... Your CPL info is NOT part of a the NCIC/WACIC file. When you run someone for CPL you also get any guns that have been transferred to them. 99% of those are just handguns that you have to fill out the DOL pistol transfer forms for from a dealer. Unless you bought one private party and got conned into doing a transfer form as well.
Also, your CPL is not public record in WA. So a landlord would not be legally able to obtain that your have one anyway unless one of your references told them about it.