Yes. A spouse in L-2 status is employment-authorised incident to status. Occupational licensing is separate: a spouse who is a licensed paramedic in Ontario will need whatever certification the state requires before working in that field, and that process should be started before the move.
Authorisation to work is not permission to practise
Two different systems have to be satisfied and only one of them is federal. Employment authorisation comes with L-2 status, so the spouse does not need a sponsoring employer and is not tied to a single job. The second system is the state's, and it governs whether a particular occupation can be practised at all.
Emergency medical certification, nursing, teaching, accounting and the trades each have their own boards, their own recognition of out-of-country training, and their own examinations. Some states have reciprocity arrangements that make the transition short; others require the full application and an examination cycle that can run past a year. The practical advice is to treat the spouse's licensing as a parallel project with its own timeline, started as soon as the destination is known, rather than as something to look into after arrival.
Children of the transferee may attend school but may not work, and dependent status ends at twenty-one.