I work at a pawn shop. Not positive if it's state law or store policy, but we keep buys for 8 days before putting them on the floor and pawns will be in the back for a minimum of 61 days. Every SINGLE item that comes in the shop has a second signed and fingerprinted document with a description of the goods along with any serial numbers. These sheets are given to the local Sheriff's office daily. Everything we take in has a holding period long enough for law enforcement to run serial numbers.
Long story short, you should have no second thoughts about purchasing a firearm from a pawn shop. And I'm sure even if by some chance a gun did turn up hot, the shop would either refund you the money or give you in store credit and a good deal on something else.