No. The household’s permissions depend on each person’s status and circumstances, not the urgency of the assignment.
Describe each person’s proposed activity
Qualifying L spouses are employment authorized incident to status, with appropriate evidence. Dependent children do not receive that work permission solely through L status. Include remote work, study and travel questions in the assessment instead of assuming the assignment covers them.
Treat the household questions as a separate review with its own list, run at the same time rather than afterwards. What is needed is each person’s intended activity in plain terms: paid work, unpaid work, study, remote work for a Canadian employer, travel back and forth. Hypothetical example: the spouse of a transferring lens-process specialist intends to continue part-time work for a Canadian optical retailer from the United States; that arrangement should be assessed on its own facts before the family relies on it, not treated as covered by the principal’s assignment.
Where a child is close to 21, note the date, since dependent eligibility ends there and an assignment planned in short renewals can outlast it. Put the answers in writing and keep them with the file. A household that has decided in advance what each person will and will not do is far quicker to advise than one improvising after arrival, and the questions are the same either way.