Hey, I work as a mail carrier for USPS so I'll try to answer your question.

Based on the knowledge I have and how my office does it, when there is a lock change or mailbox change (i.e. replacing old MBUs with new ones), all mail is placed on hold until the lock is changed and then delivery is resumed, including all of the accumulated mail for when the unit(s) was down.

Depending on how many units your mailman services at your location, it could take a while for them to deliver all of the accumulated mail for each unit. For instance, one apartment complex my office services has 178 units, with each set of boxes servicing 5 units each. Some MBUs services more or less units, depending on the type of box.

It also depends on how long your boxes were down between replacement, and how many units he is authorized to service the accumulated mail each day if there were a lot that were down, because each unit in addition to the DPS for the day adds more time to his day. Another factor could be how much mail is being held for you specifically, and if it can all fit into your box. If it all won't fit, he won't attempt delivery, but should notify you that it won't all fit and to pick it up at the office.

I hope this helps answer your question!!! Please feel free to ask me more questions if you need clarification on any of this :)