a) you live in a state where private sales are allowed and
b) it is stolen.
Moral and ethical issues aside, so what?
The only time the SN will be run through "the system" is if you commit a crime, as a compliant US citizen you "register" via some executive order or the ATF is going door-to-door confiscating now illegal guns.
Having a stolen weapon will be small potatoes at that point.
Now, addressing the moral and ethical side ...
No one of decent moral character wants to be the recipient of illl-gotten booty. However, if you purchase from some one you trust and know, then you have done due diligence (as a private citizen) in researching if the gun has a clean history.