The only thing that NICS transfers will do is document the trail of the firearm to the last legal sale of it. Once it gets into the wrong hands it doesn't matter. So it's going to make two things happen:
1- Make those who are legally purchasing a firearm jump through one more hoop (not that big a deal)
2- Give the govt just one more way to Tax/add fees to a purchase of a fire arm (just like title ship of cars)
Now don't get me wrong, I am all for a background check especially if an individual has a felonious record, or mental history. But at the end of the day, if someone wants a firearm bad enough, they will find a way to get one. The supply is to plentiful. The only thing this will allow is to say, " You sold this guy a gun. He passed the background check, went apeshit afterward, but you still sold it to him."
So unless they pass a law that would hold all previous owners accountable for said firearm, then it's a mute point. Even if they did take it to that level, the only thing they would have to say is the gun was stolen.