This is a very interesting topic actually. Here are my observations:
If you use a PO box across your citations, you will definitely encounter the problem that many sites do not allow PO boxes to be added (i.e. they do not even allow you to enter PO box, or similar phrases in the Street Address fields). However, I have discovered that Google seems to find and NOT ignore citations where the address is a PO box. When they pull the data, I can imagine they ignore the address field, i.e. they do not take it into account when parsing the collected data for a business cluster ("listing"). Thus, it would be impossible for a PO box address to show up publicly for a listing that might have been auto-generated by Google. But again - these citations are (and this is 100% sure) being discovered, and the only question is if they are being taken into account. I believe the answer to the latter is Yes.