Nope wouldnt work. If someone intent on killing people cannot legally buy the guns they will just go into the illegal market and get their unregistered gun and still commit the crime they set out to do.
However, I cannot think of anyone who would reasonably say that 100% of all people who wanted to commit a criminal act, but had difficulty purchasing a gun would go to greater lengths and effort in order to procure a gun. At least some would-be criminals would give up after an attempt to purchase a gun legally.
Or, as mentioned, felons have a higher rate of violent crime than non-felons. Statistically, since it would likely take at least a few days longer to obtain a weapon from illegitimate sources, at least one of them is going to be run over by a bus, die of a heart attack, etc.
So, of course, limiting who can get a gun reduces crime. Though, not by an appreciable amount.