Yes. A spouse admitted in L-2 status is employment-authorized incident to that status, so employment does not depend on the family finding a separate route first. Unmarried children under twenty-one may accompany the family and attend school, but they hold no work authorization of their own.
This category treats the second earner differently
The difference between derivative statuses is one of the most consequential things a household can learn early. Here the accompanying spouse may take employment, and the timing question becomes practical rather than legal: how quickly the paperwork confirming that authorization is issued and what an American employer will want to see before adding someone to payroll. Children are the part that needs a calendar.
Derivative eligibility ends at twenty-one, and a seven-year assignment started when a child is sixteen will outlive that child’s status. A household in that position should be told early that the child will need an independent basis, whether a student route or something else, rather than discovering it during an extension. Marriage must be legally recognized for the spouse to hold derivative status at all, which is worth confirming for couples who have lived together for years without marrying.