Adding to the sentence of the violent criminal is not the point. What is the point is keeping the guns out of the hands of the violent felon in the first place. This requires going after the people who are selling guns illegally to people who really shouldn't have guns. It doesn't matter if the guns are stolen - the gun-runners will still sell them as long as those guns can't be tracked back to the gun-runners. On the other hand, if all sales - public or private - are tracked with registration numbers, you will see a significant drop in gun-running...because as soon as they see the transactions can be tracked back to them, they'll either get out of the business or they'll take a much greater chance of getting caught. THAT is how to minimize illegal gun sales.
And would this make a difference? Yes, it would.
Here's what NYC has found (from the conservative New York Post):
The Bureau of Alcohol, Tobacco, Firearms and Explosives traced 8,793 guns seized in New York in 2011 and found that just 1,595 were bought in the state.
The rest came from places with less restrictive gun laws — primarily Virginia, Pennsylvania, North Carolina and Florida.
...
His criminal-justice coordinator, John Feinblatt, said the ATF’s numbers presented only a partial picture — since 85 percent of the guns used in New York City crimes come from upstate or other states.
And in the rest of the state, 68 percent of criminally used guns come from elsewhere, he said
“[In] the rest of the country, the overwhelming majority — 70 percent — come from inside the state, the opposite of our pattern,” Feinblatt said. “The lesson is pretty simple: Gun laws matter. States with strong gun laws tend to receive [illegal] guns; states with weak gun laws tend to export [them].”
Bear in mind, now, that NYC - almost certainly thanks to it's strict gun laws - is now by most measures
the safest major city in America.