Yes, this is how Snohomish does it. I did it when I reported for Jury duty. They were pleasant about it and there were no hassles at all. They asked for my CPL since I was CC at the time due to weather. I kept my holster on for the day.
I did think the bank bag was an interesting touch, but absolutely no issues with the obviously cocked and locked firearm.
When I left the officer gave me kudo's for being an armed citizen.