No. A TN application at the port of entry is decided on the spot, and a refusal for a missing certificate or a licensing gap is a real possibility. Resign only after admission, or after a petition approval if the employer filed one.
Put the border before the resignation letter
For a Canadian nurse the sequence that protects her is licence, certificate, letter, then the port-of-entry application, with the resignation and the move afterward. Each earlier step can slip. State boards miss their own estimates, the certifying organization can request a transcript that takes weeks to obtain, and the employer may need to revise the letter after review.
If the hospital wants certainty it can file Form I-129 with USCIS, which produces an approval notice before travel at the cost of time and a fee; premium processing shortens the wait for an additional charge. Some nurses prefer the port-of-entry route because it is faster once documents are ready. Either way, keep the Regina position until the U.S.
admission or approval is in hand, and tell the recruiter that the start date is conditional on the immigration step rather than the reverse. Hypothetical example: An emergency-department nurse has a confirmed offer, but the certifying organization asks for a corrected transcript two weeks before the planned move. The sensible sequence is to obtain the corrected record, have the employer confirm the revised date, and then present the completed file.
The transcript request is the record that settles the delay; a verbal assurance from the recruiter does not. A first review can identify whether direct application at inspection or an employer-filed petition better fits the employer's risk tolerance. In either route, do not resign from current employment until the relevant immigration step has succeeded.