No. A spouse admitted in TD status is not employment-authorized, and that is true regardless of the spouse's own qualifications or of how long the assignment lasts. TD dependants may attend school, which is a separate question from working.
Look at whether the spouse has an independent route
For a household where both adults work, dependent status can be a significant change, and it is better examined before the move than afterwards. The question worth asking is whether the spouse's own occupation appears among the listed professions and whether an American employer would engage them directly. That would be an independent application on its own facts rather than something derived from the principal's, and it takes its own preparation time.
Where no independent route is available, the family is deciding whether one income and the loss of the other is workable for the period involved. Children in dependent status may attend school; the age limit for unmarried children under twenty-one applies here as in other categories. Hypothetical example: Elaine accepts a laboratory-technologist engagement while her spouse, Rafi, operates a mobile bicycle-repair business.
A first family review produces a separate status plan for each person rather than assuming the principal's approval solves the household's work questions. Rafi should identify whether he has an independent immigration basis before winding down clients. The record that settles a child's eligibility is a passport and birth record showing the relationship and age, not a school enrolment letter.
Sequence travel only after each dependant's documents are assembled. Problems arise when a household budgets on dependent earnings that the status does not permit.