No. TD status permits study but not employment. A spouse who wants to work needs their own TN with their own employer letter and credential, or another classification that fits their situation.
Two professionals need two files
TD is a dependant status: the spouse and unmarried children under twenty-one may accompany the TN professional, enrol in school and remain for the same period, but the status carries no work authorization. A spouse who is also a qualified accountant, engineer or other listed professional can apply for TN independently, which means a separate U.S. employer, a separate letter describing that spouse's duties and a separate credential. The two applications can be presented at the same port of entry on the same day. If the spouse's intended work is not in a listed profession, or the only available position is with a business one of you owns, TN is not the answer for that spouse and the household should plan without that second income until another route is assessed.
Hypothetical example: a Canadian dietitian takes a TN role and her spouse operates an online tutoring business from home. The family's first review separates dependency from work permission. Marriage and the principal's admission record support TD status, but TD does not authorize the spouse to continue productive tutoring while physically in the United States. The practical choices are to pause that work, remain outside the United States, or seek a separate classification that permits it. School enrollment records and passports settle the children's dependency question; a household budget based on the spouse's unapproved income does not.