Yes, in L-2 status. An L-2 spouse is employment-authorized incident to status, for any employer, whether the principal holds L-1A or L-1B. Children may study in L-2 status but may not work.
Deciding whether the family moves for eighteen months
An assignment of this length sits at the point where families are divided on whether to move. If they do, the spouse's authorization follows from L-2 status and does not require the affiliate's involvement; the spouse should keep documentation of the status for any employer's records and may work in any field. Children may enrol in school, and a child approaching 21 should have a plan for that date because L-2 eligibility ends there.
Passports and Canadian status should be listed for each person, since a spouse or child who is a permanent resident rather than a citizen will process L-2 at a consulate. If the family stays in L'Ancienne-Lorette and the technician travels home between work blocks, that is lawful and simpler, and the family may visit as visitors, who may not work or study full time. The technician's own status has a five-year cap; an eighteen-month assignment that becomes a permanent posting should prompt a conversation about longer-term routes rather than repeated extensions.