Yes, it would. The areas of our country that have the strictest gun laws have the highest rate of gun related deaths. Countries such as the UK have higher knife related murders than we do, therefore it is safe to say that when they don't have guns, the substitute is also lethal. And last year the UK had anti-knife campaigns going. Then it will be bats, etc. You can't get rid of violence by getting rid of any potential weapon. You lower the chance of being a victim of violence by allowing each citizen the choice to defend themselves, and have strict enforcement of laws with strict penalties for violating those laws.

Yes, some form of Sandy Hook and Columbine would have happened.