In my experience I'd say that's an "it depends" type of scenario.
If two inspectors can go together, they might just go and try and talk to the guy. If only one inspector can go, (or the resident has a felony record) he'd likely call for a uniformed backer from the local police to go with him. If they pin him down, and think they've got the job accomplished, they'd likely document this, tell your PM the scoop, and that would be the end. If they miss him, or think he's a loon, I'd bet they pass that on to the police brass for that particular area as a "head's up".
The best case scenario? Your guy has a warrant for unpaid tickets, fines, other charges, and they can bring the police, then haul him to jail after the interview. Its surprising how often the "warrant God" comes to the rescue with these type of people.
From what I've heard over the last few years, the Postal Inspectors were so burdened with stolen mail, that the local police are now are working those things, which seems odd to me. Guess they are using state theft charges rather than Fed statutes. Lots of mailboxes, and blue boxes being hit looking for checks to forge. We used to love being able to say "Mail? Darn it, you gotta call the Postal Inspector."