Well…No. The people pushing for these new laws are all claiming that it is to get the guns out of the hands of criminals. They are saying these ‘common sense’ laws will get illegal guns off the streets.
In that frame, gun control laws don’t work. By definition criminals don’t care about laws and willingly break them. So no, gun control laws WON’T achieve the (public) goals these people have.
Now, if they were advocating for less accidental gun deaths and more educated gun owners the rest of your post would make sense. But they aren’t.
EDIT: NYS Sheriffs just released an amicus curiae brief against the SAFE act. On pages 21 and 22 they bring up the fact that gun control laws don’t work, since only law abiding citizens obey laws. Sheriffs SAFE Amicus | PDF | Intermediate Scrutiny | Assault Weapon