Not on the basis of TD status. A TD dependant may accompany the principal and may study, but is not employment-authorized. A spouse who wants to work needs a status of their own that permits it.
One household, two separate immigration questions
Hypothetical example: the nurse's spouse is a licensed practical nurse in Alberta and assumes the same hospital will simply hire them too. That would require the spouse to hold their own work-permitting status. If the spouse's own occupation appears in Appendix 2 and they meet its requirements, they could be admitted in their own right rather than as a dependant, with their own employer letter.
If it does not, the family should look at whether another category fits the household better, because in some categories a spouse is employment-authorized incident to status and in TD status they are not. Children admitted as TD dependants may attend school. Note each child's date of birth against the expected length of the assignment, since derivative eligibility ends at twenty-one, and confirm the citizenship of every family member rather than assuming it follows the principal's.