Answer
Yes — if a background job's next scheduled execution date falls in the past relative to the newly-restored database state, it automatically executes as soon as the database is back online and operational, rather than waiting for its next naturally-scheduled occurrence. If several jobs all become due at once this way, they're processed sequentially, which can create a noticeable delay between when a job shows as "Posted" and when it actually executes if other jobs are ahead of it in the queue.