In a word - no.
I've purchased firearms from individuals before via gun classifieds like ArmsList. The only way to check a number, according to my local police, is to bring the gun in and they'll check the number for you if you have any concerns. If it turns up hot then you loose it.
Sounds pretty stupid if you ask me.
However. When I purchase or sell a firearm I insist on seeing a valid ID and provide bills of sale with ser# etc.
I figure if a guys willing for show me his ID and sign the BoS then he's probably on the up and up. There are no guarantees though.