No. TD status by itself doesn't include work authorization, regardless of the spouse's qualifications. If the spouse wants to work, that requires a separate status or authorization assessed on its own terms, which depends on the spouse's own citizenship, profession, and the type of work intended.
Treat the spouse's case as independent
The spouse's eligibility for any work-authorizing route doesn't depend on the principal's TN approval, and shouldn't be assumed to follow automatically once the principal's case is settled. If the spouse has their own professional background, ask counsel whether it opens a separate route, and get a timeline for that route independent of the principal's TN filing. It is worth naming why the two cases are genuinely independent.
The principal's case rests on a listed profession, the applicant's own qualification, prearranged employment with a United States employer and Canadian or Mexican citizenship. The spouse's ability to work rests on a status or authorization that person holds in their own right, assessed on their own citizenship, qualifications and intended work. Neither answer follows from the other, and a favourable answer on the first tells you nothing about the second.
A first review should therefore produce two separate written positions rather than one, even where the household thinks of the move as a single decision.