No. A qualifying L spouse may be employment-authorized incident to valid status with appropriate evidence; children do not receive that benefit solely as dependents.
Review each actual admission
The principal’s title or itinerary does not itself grant relatives status. Identify their intended activities and individual records. The dependent category is for a qualifying spouse or unmarried child under 21; each person needs valid status.
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. Prepare a separate family timeline showing each dependent's passport validity, relationship record, travel plan, school need and prospective work activity. For a child, school attendance is generally the practical focus; an employment offer, paid placement, or business activity should not be assumed permissible simply because the parent holds L-1A. A larger role does not widen a dependant's permissions, and a household that plans around the promotion rather than around each person's status tends to discover the gap only after arrival. Where a spouse expects to work, discuss their position specifically rather than assuming it follows from the principal's case, and avoid long leases or resignations agreed before the structure is settled.