The provincial licence satisfies the TN credential for Registered Nurse, but a health-care worker certification is a separate admission requirement and the hospital cannot let her practise without the state licence. Entering before both exist rarely works in practice.
Separate the TN credential from the ability to practise
The regulation lists Registered Nurse with a state or provincial licence or a licenciatura, so the Quebec licence answers the credential question on its own. Two other things still decide whether the plan works. First, nurses are subject to the health-care worker certification requirement in 8 CFR 212.15, which is checked at admission and is not waived because the credential is Canadian.
Second, the employer letter must describe work the nurse can lawfully perform, and a hospital cannot assign patient care to someone the state board has not licensed. An officer who sees a letter promising floor duties, with no state licence and no certification, has reason to question whether the professional arrangement is genuine. Treat the pending licence as a gate that must open before the trip, and ask the hospital to write the letter only once it has.