Yes. An L-2 spouse is employment-authorized incident to status and can work for the affiliate or any other employer. L-2 children may study but not work, and the family's status ends when the L-1B's five-year limit or the assignment does.
Same authorization as an L-1A household, shorter ceiling
The spouse of an L-1B employee holds L-2 status on the same terms as the spouse of an L-1A manager. Since USCIS's confirmation that L-2 spouses are employment-authorized incident to status, the spouse may work with a properly annotated I-94 and no separate employment document. The affiliate could hire the spouse on the packaging line, in the office or in maintenance, or the spouse could work for an unrelated employer in the town.
Children in L-2 status attend school and may not be employed. The difference from an L-1A household is the ceiling: L-1B is limited to five years in total, so an eighteen-month assignment that becomes permanent must be re-examined before the limit, and a longer future may require a different route. If the spouse has independent specialized knowledge of the same company's processes, a second L-1B can be assessed on its own evidence.