No. TD dependants may accompany the principal and may study, but the classification does not authorize employment for a spouse or a child regardless of who is offering the job.
Each adult needs an activity of their own
Hypothetical example: TD status is derivative: it exists because the principal holds TN, and it carries the right to live in the United States and to attend school, but not to work. A spouse who intends to be employed needs an independent basis, which usually means qualifying for a classification in their own right. If the spouse is also a Canadian citizen with an offer in a listed profession, a separate TN application is the ordinary path, and it is assessed on its own merits without reference to the principal's file. Children in TD status may enrol in school. The one thing that should not happen is a spouse starting work informally on the strength of the family's presence, because that creates a status problem for the person who did it.
Plan every dependant's classification and work plan before travel, rather than treating the principal's approval as a household solution. Hypothetical example: Nora, a museum conservator accepts a TN position while her partner has a remote consulting business. TD status can permit accompanying family members to reside or study, but it does not permit the partner's paid work. They must decide if the partner needs an independent classification, keeps the work outside the United States, or delays the move.