Yes. A spouse admitted in L-2 dependent status is employment-authorized incident to that status and may work for any employer, in any field, or independently. Unmarried children under 21 may attend school but may not work.
The dependent spouse is not tied to the sponsoring company
This is one of the clearest advantages of the L route for a household, and it is frequently misunderstood as permission to work only within the transferring group. It is not so limited. The spouse's admission record annotated on arrival is what an employer asks for, and a separate employment authorization document is not required for the spouse to begin work.
Nationality does not affect the dependent's eligibility, so a spouse who holds permanent residence in Canada rather than Canadian citizenship is affected only in whether a visa is needed before travel. Children admitted as dependants may enrol in school; a child who reaches 21 must obtain an independent status, and a household with a nineteen-year-old should plan for that rather than discover it at an extension. Because L-1A is capped at seven years and does not itself confer permanent residence, a spouse who intends to build a career there should treat her own long-term status as a separate matter to raise with counsel.