Yes. An L-2 spouse is employment-authorized incident to status and may work for any employer, and a separate employment authorization document is not required for the spouse to begin.
L-2 spouses work incident to status; L-2 children do not
Hypothetical example: The L-2 spouse of a Portugal Cove-St. Philip's L-1A manager holds one of the more flexible dependant statuses. Since USCIS adopted the position that L-2 spouses are employment-authorized incident to their status, the spouse's admission record annotated as a spouse serves as evidence of work authorization, and the spouse may take a job, run a business or work remotely without first obtaining a separate card. The spouse's employment does not have to relate to the petitioning company. Children in L-2 status are in a different position: they may attend school but are not authorized to work, and their dependant status ends when they turn 21 regardless of the parent's remaining L-1A time. A child close to 21 should be considered for their own status, such as a student route, well before the birthday. The dependant's status lasts only as long as the principal's, so the spouse's job ends if the L-1A is not extended.
Hypothetical example: a refrigerated-warehousing director plans to relocate with a spouse who is deciding between employment and opening a small bakery. Before spending on the venture, the family should obtain the admission record and confirm that it identifies the spouse classification correctly. The spouse's status record supports work permission; the child's record does not create the same permission. The practical decision is whether the business can wait until admission is documented, because leases, purchases, and customer promises made before that confirmation can create avoidable commercial pressure.