Does it work
We have gun control laws but they are not being enforced as well as they should be enforced. Suicides are not mass killers and they as you point out are the main sort of gun deaths in the country. There is also a fair amount of gun deaths from gangs. These gangs also provide illegal drugs, illegal guns, human trafficking and other illegal products.
It would be more productive for law enforcement to deal with the gangs, and the illegal drugs from the drug cartels. Is gun control going to stop either of these two conditions.