No. TD status carries no work authorization of any kind, and continuing to perform work remotely for a Canadian employer from inside the United States is employment. A spouse who needs to keep earning has to qualify for a status of their own that permits it.
Remote work for a Canadian payroll is still work performed there
Households often assume the restriction applies only to taking an American job, and that logging in each morning for an employer in this province is outside it. That reading does not hold: the relevant question is where the person is when the work is done. A TD spouse may live in the United States and may study, and children admitted in TD may attend school, but employment is not available to any of them.
Three planning consequences follow. A second income has to be either abandoned for the period or rebuilt on the spouse's own eligibility, which for many people means testing whether their occupation appears on the Appendix 2 list. The relationship must be a legally recognised marriage, because a common-law partner does not qualify as a spouse here and needs a separate route entirely.
And a child stops qualifying for TD at 21, so a household with an older teenager should map that date before the move rather than at the first renewal.