Yes. An L-2 spouse is employment-authorized incident to status, which is a genuine difference from TD and one that changes household budgets. Unmarried children under twenty-one hold L-2 as well and may study, but that status does not authorize them to work.
The spouse may work; the children may not
Because dependant rules differ between categories, a household that once moved on a TN and remembers the answer from that time may plan around the wrong rule. Take the current answer for the category actually being used, and keep the evidence of status for each dependant in the family’s own file rather than the employer’s. A child’s twenty-first birthday matters here in a specific way: derivative status for unmarried children ends at that age, so a student who will cross it during the assignment needs a plan of her own, arranged in advance and not in the week it takes effect.
Hypothetical example: an operations executive at a roof-truss and wall-panel plant near Roxton Pond is transferred for three years. Her spouse intends to keep working, and their elder child is twenty years and seven months old at the time of filing. The household needs three separate answers rather than one. The spouse’s work authorization follows from L-2 status. The younger child may study as a dependant. The elder child needs a route that does not depend on age, and the sensible time to identify it is now, while there is still a year in which to arrange it calmly.