Permits are hard to verify as you need not only the permits, but also the blue prints.
For example I had a property where the permit may said "New Kitchen sink." That is actually pointing at a blueprint for a complete remodel a flight of stairs and three bedrooms added up stairs.
I had listed the house and the buyer's agent announced all the work was not permitted, accept of course for the kitchen sink. The city will not release the blue prints saying that it is intellectual property of the Architect. Luckily I found the blueprints upstairs in the attic, or that deal would have fallen apart.
Code violations are different. If there are code violations, you know that the city did not inspect, and so they probably did not pull permits.
If you buy a home, and the seller did not tell you that the room was permitted you have two years to back to him and get him / her to fix that. But no, no one pulls permits it is an exercise in futility. The termite inspector and home inspector will usually notice many items that are not to code which is the red flag t hat permits may not be on file.
If the room needs to be removed you can sue the seller for not telling you, for the cost of the removal or room and the decrease in the value due to less square footage. Or you can go to the city and get the inspection and bring it up to code. The city may refuse and force you to remove the room at that point.