For the immigration category, yes: Registered Nurse requires a state or provincial licence or a licenciatura degree, and Ontario registration is a provincial licence. It does not permit practice in New York, which is a state licensing question the employer must address separately.
Two licences, two decision-makers
Hypothetical example: a South Frontenac nurse holds current Ontario registration, a bachelor's degree in nursing and an offer from a New York hospital network. The TN profession list treats a provincial licence as sufficient for Registered Nurse, so her immigration file is not missing a credential. The state board, however, decides who may practise in New York, and the hospital will not roster her until that licence exists or the board has confirmed a status the employer accepts.
The sequencing question is therefore practical rather than legal: which comes first, the state licence or the TN admission? Many employers want the state licence in hand before writing the TN letter, because the letter describes work she must be able to perform lawfully. Ask the recruiter directly which document they need first, and confirm that the TN letter will describe registered-nurse duties rather than a broader care-coordination role that might not fit the listed profession.
A first review should turn the offer into a duty-by-duty comparison with the TN profession rather than relying on a job title. Hypothetical example: a Canadian medical laboratory technologist is recruited to validate blood-analysis procedures for a private laboratory. Her degree record and official transcript settle the education point; the laboratory's detailed duty list settles whether the work is genuinely technologist work.
If the actual assignment is chiefly sales, scheduling, or general office supervision, the employer must change the role or choose a different route before making travel plans.