Yes. An L-2 spouse is employment-authorized incident to status and does not need a separate employment-authorization document to work, although she may obtain one for convenience. Children in L-2 status may study but may not work.
L-2 spouses work; L-2 children do not
This is one of the practical differences between a company transfer and a TN offer. Since USCIS recognized L-2 spouses as employment-authorized incident to status, an L-2 spouse may accept any lawful employment once admitted, with the admission record itself serving as evidence of authorization. For a Kent household, that means the manager's wife, who might work in health care or bookkeeping, can plan on earning rather than waiting for a category of her own. Children in L-2 status may attend school, but they have no work authorization and cease to qualify at twenty-one or upon marriage. None of this applies until the principal's petition is approved and the family is admitted; a spouse who arrives as a visitor to look for work is in the wrong status. Keep each family member's passport, admission record and, if obtained, employment-authorization document together so an employer's verification is straightforward.
Hypothetical example: a fisheries-logistics director transfers with a spouse who has a signed U.S. job offer beginning two weeks later. The first review confirms that the spouse will be admitted in the appropriate dependant classification and that the employer can verify the admission record. The job offer itself does not confer status. If a child will turn twenty-one during the assignment, the family should calendar that date instead of assuming the child's status lasts for the full transfer.