No. A port-of-entry application is decided on the spot and can be refused; giving notice beforehand converts a refusal into unemployment.
Sequence the resignation after the admission, not before
Hypothetical example: Because a Canadian citizen can apply for TN at the port of entry, the timing question for a Portugal Cove-St. Philip's applicant is different from a petition-based route. The file can be prepared, the state licence pursued and the employer letter finalized while the applicant continues working in St. John's. The sensible order is: confirm the state licence position, obtain the final employer letter with a start date that allows travel, arrange leave rather than resignation if the employer permits, present the application at the port, and give notice only once admitted in TN status. If the employer insists on a fixed start date that cannot move, ask for that date to be written as conditional on admission. An applicant who is refused can address the deficiency and reapply, but only if there is still a Canadian job and a valid offer to return to.
Hypothetical example: a recreation therapist has a U.S. rehabilitation-centre offer that requires a state credential before the first patient visit. The useful first review produces a dependency list: the employer's final letter relies on a feasible start date, the start date relies on credential processing, and travel relies on a complete TN file. Request a conditional start date and keep the present employment until admission is granted. The state board's written requirements, rather than the employer's hoped-for timetable, determine whether the proposed sequence can actually occur.