Yes. Dependants of L-1B and L-1A transferees hold the same L-2 status: spouses are employment-authorized incident to status, children may study but not work, and children lose status at 21.
Same dependant status, shorter principal clock
The L-2 rules do not distinguish between the two L-1 subcategories. A spouse accompanying a Lac-Beauport L-1B transferee may take employment in the United States on the strength of the status itself, and the admission record annotated for an L-2 spouse serves as proof for an employer. Children may enrol in school at any level but may not work, and their status ends when they marry or reach 21.
The practical difference for a family lies in the principal's timeline. L-1B is limited to five years, compared with seven for L-1A, so a family planning around the maximum period should use the shorter figure unless a later promotion into a managerial role is realistic and documented. A change from L-1B to L-1A requires a new petition and does not extend the total time already used.
Compare every family member's admission record after each entry.