No. The classification concerns admission and permission to work in the professional role; the right to practise veterinary medicine comes from the state licensing authority. Both are required, they are granted by different bodies on different timetables, and satisfying one says nothing about the other.
Two permissions, two authorities, two schedules
Set them out as parallel tracks. The licensing track begins with the state board: an application, verification of the degree from the issuing institution, examinations where required, possibly an interview, and a board decision that may only be made on scheduled dates. The immigration track begins with the employer's letter and the qualification documents, and it can move quickly once those exist. Because the board's schedule is rarely flexible and the immigration route often is, plan the licence first and fit the classification behind it. Ask the employer what role, if any, exists for the veterinarian before the licence is granted, and be careful with the answer: work that requires a licence cannot be performed without one, and describing it as observation or training does not change what it is.
Hypothetical example: a Tyendinaga landscape architect has a degree but will stamp plans in a state that reserves that act to licensees. A first review separates the listed-profession qualification from the state permission. The degree transcript settles the former; the board's written rule and licence record settle the latter. If the offer assumes sealed plans on day one, delay or redesign the duties rather than hoping a classification solves professional regulation.