No. TD dependants are not employment-authorized by that status. They may generally study, and a spouse who wants to work needs an independent basis for work authorization.
Study is permitted; employment is not
This is one of the few points in the TN framework where the answer does not depend on documents at all, and it surprises households that assumed a family move meant two incomes. Dependants in TD status may generally attend school, and the published guidance on which nonimmigrant classes may study is the reference to check for the specific circumstances. Employment is different: dependent status does not carry work permission, and no letter from the principal's employer changes that.
A spouse who intends to work needs a route of their own, assessed on their own facts, which may be a separate TN if their occupation is listed and they hold the qualification, or another category entirely. Planning the household budget on one authorized income is the realistic starting point.