Does a background check mean that it is registered that you actually have the gun ?
If it didn't before, you can bet it does now.
As others gave said it just means you expressed an interest in a firearm and the dealer ran a background check to make sure no disqualifiers turned up. It does not mean you completed the transaction. On the other hand if the dealer actually sells you a firearm he has a hard copy DROS/4473 (Dealers Record of Sale) on file. All that means it is the last recorded sale of the firearm. What you do with it after that is your business depending on the state you live in . California for example want all transactions to go through a dealer. I wouldn't get to worried yet. If reports start turning up that the BATFE is starting to review all U.S.dealers books then I would be concerned but that would be such a monumental task as to be almost impracticable.
The choke point would ammunition rather than firearms. Without ammo a firearm will an expensive paperweight.