No. Washington State does not let landlords evict tenants without following the proper court eviction process.
The landlord must give you a proper written "termination" notice before starting an eviction lawsuit. The 14-day Notice to Pay Rent or Vacate is one type of termination notice.
If you are still living in the place after 14 days, and you still owe rent, the landlord may then start an eviction lawsuit. The landlord does this by giving you official court papers called a "Summons" and "Complaint." These papers may require you to send a response to your landlord or their lawyer.
The landlord must win an eviction lawsuit and get a judge to sign an order directing the sheriff to evict you. Only the sheriff can formally evict you or change the locks on the rental.