Not directly, since dependent eligibility rests on the family relationship. It matters indirectly: if the departure destabilizes the offer itself, family plans built on that offer are exposed, so hold irreversible commitments until the employer confirms the role.
Confirm the job before the household moves
Families often act on a start date by giving notice on a lease, enrolling a child, or ending a spouse's employment. A signing manager's exit is a reasonable moment to ask the employer to confirm in writing that the position and start date stand. A spouse and unmarried children under 21 may qualify for TD, which permits study but does not authorize employment, so a second income cannot be assumed.
What a first review turns up here is a lease already terminated. The household acted on a start date the departing manager gave verbally, and there is now nobody able to reconfirm it. The record that settles the question is a written confirmation of the start date from the successor, dated after the departure, and it is worth waiting for before anything irreversible is signed.
The dependent condition is untouched by any of this and should not be re-argued: a spouse and unmarried children under 21 may qualify for TD, which permits study but does not authorize employment. Hypothetical example: an Accountant joining a pension consulting practice holds the school registration until the successor confirms the September start in writing, then enrols the following week without penalty.