No.

RCW 46.04.304
Moped.
"Moped" means a motorized device designed to travel with not more than three wheels in contact with the ground and having an electric or a liquid fuel motor with a cylinder displacement not exceeding fifty cubic centimeters which produces no more than two gross brake horsepower (developed by a prime mover, as measured by a brake applied to the driving shaft) that is capable of propelling the device at not more than thirty miles per hour on level ground.


RCW 46.04.071
Bicycle.
"Bicycle" means every device propelled solely by human power upon which a person or persons may ride, having two tandem wheels either of which is sixteen inches or more in diameter, or three wheels, any one of which is more than twenty inches in diameter.



RCW 46.61.710 prohibits the operation of mopeds on a "bicycle path or trail, bikeway, equestrian trail, or hiking or recreational trail."

Bikeway == bicycle lane.
No mopeds, no scooters, no motorcycles.