Yes. A spouse admitted in L-2 status is employment-authorized incident to that status, so the spouse may accept employment without a separate application for permission to work. Children admitted as dependants may study but are not authorized to work, and their status ends when they reach twenty-one.
Confirm what the employer will ask to see
The legal position is settled, but the practical one involves a document a US employer will want in its hiring file, so the spouse should be prepared to explain the basis of employment authorization and to produce the admission record showing L-2 status. Where the spouse holds a professional licence issued in Ontario, check whether the state in question recognizes it or requires its own examination, because employment authorization and professional licensure are different gates and satisfying one says nothing about the other. For the children, put each birthday on the same calendar as the principal's status expiry, and plan a year ahead for any child approaching twenty-one, since a change to a student or other category takes preparation and cannot be arranged in the week the birthday arrives.
Hypothetical example: a sound-engineering manager transfers while his spouse has a pending offer from an American studio. They should preserve the spouse's L-2 admission evidence and have the studio confirm its onboarding records before a start date is fixed. Prepare a household calendar with the principal's validity date, each child's age-out date, and any professional licence deadline.
The first review should identify work, study, and travel plans separately. Confusion arises when a family assumes the principal's approval automatically supplies every document an employer or licensing body may request.