Does this device come with certification / calibration paperwork of any sort?
Nope, at least not the PAA3 doesn't. There are no tolerances on the published specifications. It's a tool, not a lab instrument. You take it along on a PA job or a room assessment. You don't use it to determine if you need to sue the factory for too high a noise environment or the airline for flying too close to your house.
That's why it only costs a few hundred bucks, I guess.