Not on the basis of TD. A Canadian company and Canadian pay do not authorize the spouse to perform employment from inside the United States; TD prohibits that remote work too.
Explain the service location to the Canadian employer
Keep the employer’s payroll decision separate from its proposed remote-work arrangement. Identify where the spouse will actually perform the services, which dates are contemplated and what the household assumes about continued earnings. A qualifying spouse or unmarried child under 21 may accompany in TD, but neither obtains work rights from it. If an independent U.S. work route is proposed, have its own eligibility and permission assessed before relying on the arrangement; the principal’s TN case cannot answer it. Do not describe unchanged Canadian withholding or an existing employment contract as evidence that the spouse’s U.S.-performed work is authorized.
If the profession match is uncertain, avoid finalizing school enrollment, housing, or a spouse's own plans around a start date that assumes TN is confirmed. Dependents' documents are about relationship and identity, so a spouse and unmarried children under 21 typically need marriage and birth records rather than educational ones.