Prior to the laws about background checks there was no registering guns in Texas. 

It takes longer to fill out the application to purchase a gun than for the sales person to put one's name, SS#, etc. into a computer and get the results.  If one is a law abiding citizen (in TX) a gun purchase could take about 15 minutes.  Took me longer to decide what weapon I wanted to purchase than to have the background check done.

In 1977 I inherited two hand guns and not knowing I called the state office to find out about changing the registrations and was told there was no registering guns in Texas. So today when purchasing a gun legally it is not registered with the state, but with the US Federal government. 

The FBI does the background checks, so I guess in reality the FBI keeps the serial number of the guns purchased legally today on file.  The FBI gets your fingerprints as part of a background check, if you apply for a concealed handgun license (CHL), but not when a gun is purchased.

Don't know how catalog sales of firearms would be handled for sure. 

When a firearm is purchase online legally the gun has to be shipped to a registered firearms dealer or a Federal Firearms License holder (FFL).  So a firearm can be purchased without having to go to a gun store or show.  So I would imagine catalog sales would be the same.

A background check would still be done for legal purchase of a firearm either way.