Yes. Spouses and unmarried children under 21 use L-2 status in both cases. The spouse is employment-authorized incident to status; children may study but not work, and they lose derivative eligibility at 21.
What usually goes wrong
What goes wrong is not the rule but the assumption that the principal's shorter maximum stay does not matter to the family. Hypothetical example: a Lévis naval-architecture specialist takes a three-year L-1B assignment, and the household plans around a five-year stay because a colleague on L-1A mentioned seven years. L-1B is capped at five years in total, including any prior L time, and every dependant's status ends when the principal's does.
A spouse who builds a U.S. practice on L-2 employment authorization and a child who enters a four-year degree should both plan for the principal's real ceiling and for what replaces it. A child who turns 21 before the assignment ends needs a status of their own, most often a student status, arranged before the birthday rather than after.
Record each person's passport, relationship evidence and birth date at the outset.