No, it doesn't, because if the bureaucratic system is dysfunctional, then the legislated solution is to block the sale of weapons.
I haven't heard the outcome, but the Pennsylvania instant check system was going to be "updated" which supposedly required a several day period in which NOBODY could purchase a firearm. Except, I am sure, our masters, the law enforcement community.
If I go into Wal Mart and buy a gun I have to wait at the counter until the paperwork is sent through. If I lay my money down on the counter and walk off, I'm going to jail and have probably committed a federal offense.
On the other hand, if I make a private purchase from my next door neighbor, I give him the money he gives me the gun. The government doesn't know I have bought a weapon. No clearing house to go through.