Yes. An L-2 spouse is employment-authorized incident to status, and the admission record itself serves as evidence of that authorization. Children in L-2 status may study but may not work.
The spouse's authorization comes with the status
This is one of the practical differences between L-1 and TN for a Mount Pearl household. The spouse of an L-1A manager is admitted in L-2 status and, under current policy, is considered employment-authorized incident to that status; the Form I-94 annotated for an L-2 spouse serves as evidence of authorization for an employer's Form I-9. The spouse may therefore take a job, contract or run a business without first obtaining a separate employment authorization document, though some spouses still request one for convenience. Children admitted as L-2 dependants may attend school but are not authorized to work, and each child's status ends when the child turns 21 or marries. The family's status is tied to the principal's, so if the L-1A employment ends, the dependants' basis for staying ends with it. A spouse who wants to keep a Mount Pearl business running remotely is in a different position than a TD spouse, but should still confirm that any Canadian tax and licensing obligations are handled.
Hypothetical example: a commercial-laundry company's regional director plans to transfer with a spouse who wants to open a small online retail business and a nineteen-year-old child in college. The family should obtain and retain each admission record after entry. That record settles the spouse's L-2 classification and work-authorization evidence; the child's age and marital status control dependent eligibility. Before the child approaches 21, the household should evaluate a separate student or other status rather than assume an extension of the principal's L-1A will solve it.