For the TN qualification itself, a provincial licence satisfies the Registered Nurse entry. The Washington licence is the employer's condition of employment, and an officer may ask how the applicant will lawfully practise from day one. Carrying both is the strongest course; without the Washington licence, a still-conditional offer may not establish that the prearranged job is actually available.
Two licences, two purposes
The USMCA entry for Registered Nurse asks for a state or provincial licence or a Licenciatura degree, so British Columbia registration meets the treaty requirement. The problem arises at the port of entry, where an officer reads the offer letter and sees that the hospital requires a Washington licence. If the applicant cannot show that licence, or at least a formal temporary permit from the state board, the officer may question whether the prearranged employment is actually available.
Hypothetical example: a Lake Country nurse arrives with her BC registration and an offer letter that says employment is conditional on Washington licensure; the officer asks for the licence and she has only an application receipt. The remedy is sequencing: file for endorsement first, get the offer letter reworded once the licence issues, and only then travel. Nothing in the law changes between those steps, but the evidence does.
A first review should produce an evidence map with four entries: the treaty qualification, the credential required by the hiring entity, the issuing authority for each record, and the date on which each record is valid. The active registration lookup or formal permit from the licensing authority settles the practice question; an application receipt merely shows that a request was made. Compare that record with the exact wording of the offer before choosing an application date.
Hypothetical example: a Lake Country architect has British Columbia registration and an offer from a Montana design firm, but the letter says she cannot sign drawings until her Montana credential is issued. The review separates her TN qualification from that employment restriction, obtains the board's written status, and asks the firm to state the duties she may lawfully begin. Travelling before that point invites a finding that the described employment is unavailable.