During the season, on legal days with legal equipment and a valid license. Check the WDFW website for regulations.
If the area is open and it's the right day of the week for crabbing then yes but no matter anyone's answer here you should check on the Washington fish and game website to know for sure (https://wdfw.wa.gov). Make sure you have your shellfish license. It looks like is open now but read here to be certain. I think the park is in 8-2. https://wdfw.wa.gov/fishing/shellfish/crab/
Thanks! Your answer is awaiting moderation.