The tracking would be alleviated because they would go into a queue and your UCP toolbar will alert you, and any other administrative staff who has such permissions, that there are posts needing moderation. And, as Jim alluded to, since the member in question has been duly notified, I would not give priority to having to review them.
Letting them sit and becoming a bit stale might motivate the member to get with it. You do however want to process them with some expediency because you do want to incentivise him/her. Judgment call as far as how much time to let elapse.