No. Dependants admitted in TD status may live in the United States and may study, but the status carries no work authorization at any point and no permit converts it. A spouse who needs to earn must qualify for a status of her own that permits employment.
TD covers residence and study, never employment
Derivative TD status exists only while the principal holds the professional status, and it authorizes no work of any kind. That restriction is broader than families expect: it reaches an American job, freelance work, and continuing to work remotely for a Quebec employer from inside the United States. Two details govern who even qualifies as a dependant.
The relationship must be a legally recognized marriage, so a common-law partner is not a spouse for this purpose and needs a separate route. A child qualifies while unmarried and under twenty-one, and eligibility ends at that birthday rather than at the next renewal. Hypothetical example: a statistician from the municipality accepts an American analytics post while his wife, a Quebec-licensed nurse, assumes she can pick up shifts once they arrive.
She cannot, and where a second income is essential the household should compare categories whose spouses are employment-authorized incident to status. A household relying on two incomes should settle this point before a lease is signed on either side of the border.