Well, I did it yesterday
I tossed it in the box outside after going in and seeing a 15 person line at the counter (all of them looking like they'd been there a while). The only thing the box said was that it must weigh under 16oz, so away I went. It didn't say "No Priority Mail" or anything else. When I went inside there was an automated label and postage center that printed a label AND a postage strip for your package. Next to this "mail center" there was a parcel receptacle, but it said "only for packages with automated label AND postage. So since I printed my own postage strip a the office on my meter I was SOL.