Not automatically. TD status does not itself authorize employment, regardless of who the client is or where they are located.
Review the spouse's own work plan separately
Document the spouse's intended remote work in detail and confirm whether a separate work authorization route applies, rather than assuming a Canadian client relationship is irrelevant.
Treat the accompanying spouse's activity as work even when services are delivered online, compensation stays in Canada, and the customer has no U.S. office. A TD spouse or child cannot work in TD status, although either may study; either may work if otherwise authorized by DHS. Record the spouse's citizenship, employer, duties, physical work location, pay arrangement, and any separate status or authorization before promising continued availability to the client. Also confirm that the principal is a Canadian or Mexican citizen—not merely a Canadian permanent resident—and has prearranged professional activity in a profession in Appendix 2 to Annex 16-A of the USMCA with its required credential. The common mistake is analyzing only where the client sits rather than what the spouse will do while physically present.
Hypothetical example: A seed laboratory hires an agricultural chemist living around Tecumseh for qualifying U.S. professional work, while the accompanying spouse plans to keep preparing monthly payroll forecasts for a Canadian restaurant group. The couple separates the principal's TN evidence from the spouse's proposed consulting calendar. Unless the spouse obtains independent DHS work authorization, the forecasts pause during time in TD status; studying an accounting course would be permitted, but delivering paid reports would not.