Yes. An L-2 spouse is employment-authorized incident to status and may work for any employer, including the affiliate itself. Children in L-2 status may attend school but may not work.
L-2 work authorization is a real advantage over TN for this household
The spouse of an L-1A transferee is admitted in L-2 status, and current policy treats an L-2 spouse as authorized to work incident to that status, with the annotated admission record accepted by employers as evidence. She may take a job with a local employer, work for the affiliate, contract, or start a business, and does not need to obtain a separate employment document first, although some spouses request one for convenience. Unmarried children under 21 hold L-2 status too; they may study and may not work, and each child's status ends at 21 or on marriage.
Everyone's status depends on the executive's L-1A continuing, so a decision to sell the affiliate or to step back would end the family's basis for staying. If the spouse is not a Canadian citizen, she will need an L-2 visa from a consulate before travelling, but her work authorization on arrival is the same. For a Paradise household comparing routes, this is often the fact that settles the choice.
A first review should produce a separate status and activity list for each family member, using passports, the marriage certificate, birth certificates and each admission record. Hypothetical example: the spouse of a conservatory-plant importer plans to accept a job after arrival; the annotated I-94, rather than the principal’s approval notice, is the record the new employer needs to inspect.