Yes, but only if they have a work permit.
Your sponsored spouse or partner can apply for an open work permit if
they’re living with you, in Canada, and
we’ve confirmed their application for permanent residence is complete
While your spouse or partner’s permanent residence application is being processed, they must
maintain legal status as a temporary resident in Canada, and
wait for their work permit application to be approved before starting to work
If they already have a work permit that is expiring, they can keep working as long as they maintain their status as a worker.
How to apply for this open work permit