Not in dependent status. A spouse and unmarried children under 21 may accompany a TN holder in TD status, and TD permits study but does not authorize employment of any kind. If your spouse intends to earn income in the United States, that requires a separate status obtained on its own merits.
Two adults, two separate routes
The practical trap is a household that budgets on two salaries. Hypothetical example: a psychologist accepts a TN position at a clinic in New Hampshire and her husband, a cabinetmaker with twenty years in a Saint-Cyrille-de-Wendover millwork shop, assumes he will pick up bench work once they arrive. He cannot do so on TD, and he cannot fix it by applying for his own TN, because cabinetmaking is a trade with no Appendix 2 entry.
His realistic options are an employer willing to sponsor him in some other classification for which he qualifies, or a decision that he does not work in the United States for now. Children in TD may enrol in school, which usually removes the other half of the household worry. Two further points are worth diarising: the derivative limit is unmarried children under 21, so a birthday can end a child’s eligibility mid-posting, and each dependant’s status is tied to the principal’s, ending when that status ends.