Yes, if you are hit by another vehicle and they are at-fault then you do have the right to make a claim.
Just because you do not have a motorcycle endorsement on your Washington driver's license does not mean you were at fault for causing the accident. Not having the endorsement does not prevent you or dismiss your legal rights in a motorcycle accident. Your right to receive compensation for your medical bills or the damage to your bike remains.
If you've been injured a motorcycle accident, don't have a motorcycle endorsement on your license, and aren't sure what to do or what to say to the insurance adjuster. Stop, and order my book Motorcycle Accident Secrets Unlocked before signing any forms or giving a recorded statement. Or if you need help now call 888-230-4970.