No, having Liability and physical coverages of Collision and Comprehensive, thus full coverage, will not be accepted by Washington State if they are requiring you to obtain and maintain a SR-22.

In WA if a driver is required to obtain an SR-22 then he or she must normally maintain it for 3 years. The reason that you are required to acquire the SR-22 may change the amount of time you are required to carry it though. You can be mandated by the state to get a SR22 for a variety of reasons from a driver's license suspension reinstatement due to a DUI, accident without insurance or a second or subsequent offense of leaving a child unattended in a running vehicle, to name a few.

Typically in WA when you are eligible to reinstate your driver license, you must file future proof of financial responsibility, also known as an SR-22, for 3 years from the date you are eligible to reinstate your driver license for that incident.

Already having full coverage auto insurance on your vehicle is a good thing but when WA requires you to have your insurer submit a SR-22 form that shows you have specific coverages you must do so and not just submit a copy of your full coverage car insurance policy to the state.

With a SR-22 your insurer will inform the state when your coverage starts and if you take off the coverage they will inform the state so that the WA DMV can take actions against you if you are still required to carry the SR-22. The SR-22 form is basically the state's way of making sure you keep at least Liability coverages on your vehicle per their requirement due to whatever event mandated you to get this certificate of insurance filed with the state.

Your full coverage auto insurance policy just shows that you are currently insured while the SR-22 form is called future proof of financial responsibility because the insurer files the form when you start the coverage and will inform the WA DMV if you take off the required coverage.

Your current insurance coverages may comply with what coverages are required for an insurance company to file the SR22 with Washington State on your behalf however you would need to speak with your agent about filing this financial responsibility form. If your current insurer does not file SR-22 forms with the state than you will need to look elsewhere and get your coverage with an insurance carrier that does offer SR-22 filing. If you need to get a SR-22 you can start here getting quotes for Washington State car insurance.