Yes. An L-2 spouse is employment-authorized incident to status under current USCIS policy, and the Form I-94 annotated for L-2 spouses serves as evidence of that authorization. Children in L-2 status may study but may not work.
The L-2 spouse rule is the most generous of the transfer categories
Among the categories on this site, L-1 gives an accompanying spouse the most freedom. Dana's husband, in L-2 status, may work for any employer or for himself without first obtaining a separate employment authorization document, because the authorization is incident to his status; the annotated I-94 is the proof most employers ask for when completing their onboarding verification. He can also study.
Their children, if unmarried and under 21, enter in L-2 status too, can attend school, and cannot work. The family's stay is tied to Dana's, so if her L-1A ends because the U.S. plant is sold or she leaves the company, the L-2 statuses end with it and any job her husband holds must stop.
If a child is approaching 21, plan that child's own status ahead of the birthday. Note that the marriage must be legally valid; a common-law spouse does not qualify for L-2. Hypothetical example: Yara is transferred from a Canadian marine-insurance administrator to lead its U.S.
affiliate, while her wife plans to start a design business. The couple should save the I-94 records, marriage certificate and the principal's approval notice together, then have an employer review the spouse's current acceptable I-9 evidence before a start date is promised. A child near 21 needs a separate timeline.
The underlying transfer still requires the principal's qualifying year and supports only up to the seven-year L-1A maximum; family planning cannot extend either limit.