No, and this is the point that catches families out most often. A spouse and unmarried children under twenty-one accompany the principal in TD status, which permits residence and full-time study but confers no employment authorisation. A spouse who intends to work needs an independent classification of their own, obtained on the strength of their own offer and qualifications.
TD is a residence status, not a household work permit
This is the most frequently misunderstood point in the whole classification, partly because L-2 and E-2 spouses are treated differently. A TD dependant may enrol in school or university, may hold a bank account and may live in the United States for as long as the principal's admission runs, but any employment, paid or unpaid in substance, is outside the status. Working anyway puts both the dependant and the principal's file at risk.
Hypothetical example: a statistician from Sainte-Cécile-de-Milton is admitted under the Mathematician entry, which covers statisticians, to work for an agricultural analytics company. Her husband is offered part-time bookkeeping work near their new home. He cannot accept it in TD status.
If bookkeeping is what he wants, the questions become whether his own occupation appears in the appendix at all, and whether that employer would file a petition in some other classification.