Not from inside the United States. TD dependants may study but may not work, and preparing books for Canadian clients while physically in the U.S. is work regardless of where the clients or the bank account are located.
Where the work is done, not where the client sits
Hypothetical example: the applicant's spouse runs a bookkeeping practice from home in Oromocto and plans to keep her clients after the move. TD status does not authorize employment, and the location of the client does not change that; the services would be performed in the United States. She may study in TD, and she could look at whether her own qualifications support an independent route, for example the accountant entry on the USMCA list if she holds the required degree and a U.S. employer offers a prearranged position. A Canadian permanent-resident spouse who is not a citizen cannot use TN at all. Each family member's own activity determines the route, and the principal's approval does not extend work permission to anyone else. Children in TD status may attend school but are also barred from employment.
Hypothetical example: a theatrical lighting designer plans to continue accepting online design commissions after joining a spouse in TD status. The client contracts, invoices, and work calendar settle the point: producing designs while physically present in America constitutes work even when the clients pay abroad. First decide whether the commissions will stop, be completed before travel, or be handled by someone outside the country without the spouse performing services there. If the spouse needs to work, review an independent category before relocation rather than assuming the principal's TN approval helps. Keep school enrollment separate from employment; study is permitted, but it does not convert freelance activity into permitted activity.