No it doesn’t. As has been show repeatedly, there isn’t a correlation between less guns and a safer society. You and I can both find examples of countries with strict gun laws and high rates of violence, easy availability of firearms and low levels of violence, easy availability of firearms and high rates of violence- we can go around the world and find examples to suit a theory.
The real driver is the willingness of a person or persons to commit acts of violence. The prohibition of the law abiding to have the effective means to defend themselves just makes them vulnerable to those willing to act in an evil manner. The disarmament of the Jews, or the Russian officers during the revolution, or the Russian peasants under Stalin, or the Chinese peasants under Mao just made them more vulnerable to those who wished to do harm. Unless of course one believes that government killing of its own people doesn’t factor in to the definition of a safer society.
Or perhaps I misunderstand- are you stating that by fewer guns you also mean disarmament of the government?