Does USPS accept addresses printed on to boxes?

Our company is forcing us to remove label shipping entirely and print addresses through a printer we have directly onto envelopes. Over 90% of our shipments are based on boxes for filling material. I've already tried printing directly onto boxes and to a degree it works despite it may not be recommended for the practice we have.

I can't find a straight answer on the United States Parcel Service site or forums but would they accept address information printed directly onto brown boxes?