I would assume that part of the transfer involves checking the serial number against whatever database the police use, but so many gun laws are poorly thought it I wouldn't be completely shocked if it's not.

I'm guessing it would be flagged, and then the FFL probably has some responsibility to notify police etc. and the person who tried to sell it would probably face criminal charges. Is there any risk to the buyer? I.e. If I tried to buy a handgun from someone on Armslist that turned out to be stolen, is there any risk that I could get in trouble? (assuming I didn't know it was stolen, of course)