No. Qualifying L spouses may work incident to valid status with appropriate evidence; children do not receive that benefit solely as dependents.
Assess the actual person and activity
The principal’s expertise or project need does not change family status rules. Review each relative’s plans separately. The dependent category is for a qualifying spouse or unmarried child under 21; each person needs valid status.
Under current USCIS policy, the spouse of an L-1 transferee is authorized to work by virtue of L-2 status, evidenced by an admission record carrying the spousal notation, without applying for a separate employment authorization document. A spouse who intends to work should confirm in advance what an American employer will want to see as proof of authorization, because status-based authorization is less familiar to payroll departments than a card. What is needed is each person’s intended activity in plain terms: paid work, unpaid work, study, remote work for a Canadian employer, travel back and forth. The usual mistake is treating petition approval as proof that every relative already holds the correct status or may begin employment.