I can't speak for every police agency, but we rarely run an ATF trace on a firearm that's turned in or found. I will run an NCIC check, otherwise it's placed in evidence as found property.
Now if it was found in a sleazy "don't ask" hotel then we may... especially if it's obvious that the previous room occupants are up to no good. For the most part, we don't run a trace unless the firearm was recovered from a gang banger CCW or used in any other crime.
FWIW, I giggle when we recover Brycos, Jennings, or Lorcins. When I get a high point, or especially a glock, off of someone... well it worries me that they have something that is more likely to work properly and hurt me than it is to blow up in their hand.