I believe, so long as the Second Amendment stands unmodified in the Bill of Rights, any proposal to implement anything like that would be met with reasonable armed resistance.
To strictly answer your question though, I think we need only look at countries that have a disarmed citizenry. Of course, gun crime goes down, but is not eradicated. Instances of other types of violent crime go way up to bring the overall crime rate at a similar level as it was when gun crime was common.
My personal opinion however, while I only own Black Powder weapons, is that the legislation we do have on the table is the root cause for the increase in gun related crime. Our citizenry is overall uneducated about the proper usage of the Second Amendment, which has led to a decline in individuals willing to carry with a purpose, in defense of the State (the People)
