Does the mailbox law apply to PO boxes too?

Yes. PO boxes are owned and operated by the USPS, so the same federal restriction that protects residential mailboxes applies to them.

• Federal jurisdiction: placing anything inside a PO box without going through the postal system is a federal offense.
• No marketing exception: flyers, cards, and other promotional material cannot be dropped in without proper postage.
• Applies to every mail receptacle: residential boxes, cluster boxes, and PO boxes alike.

The compliant way to reach those recipients is through the mail stream itself. Direct mail lets you land in the box legally, with postage and full delivery tracking.