If only we had a study with real-life data to assess that question. Oh wait, here is one: Chapman, S., Alpers, P., & Jones, M. (2016). Association Between Gun Law Reforms and Intentional Firearm Deaths in Australia, 1979-2013. JAMA, 316(3), 291. http://dx.doi.org/10.1001/jama.2016.8752
Question: What happened to the trend in firearm deaths after Australia introduced extensive gun law reform in 1996, including a ban on semiautomatic rifles and pump-action shotguns?
Findings: In the 18 years before the ban, there were 13 mass shootings, whereas in the 20 years following the ban, no mass shootings occurred, and the decline in total firearm deaths accelerated.
Meaning: Implementation of a ban on rapid-fire firearms was associated with reductions in mass shootings and total firearm deaths.
So, apparently, in Australia it did. But, is there any evidence of a correlation between gun ownership and fire-arm related deaths? Is a r=0.80 with a p<0.0001 sufficient for you? Bangalore, S., & Messerli, F. (2013). Gun Ownership and Firearm-related Deaths. The American Journal Of Medicine, 126(10), 873-876.
So, where do we stand on evidence-based gun policies? Still, if you can’t understand why the USA hasn’t banned guns yet, you might wanna read The Gun Control Debate: Why Experience and Culture Matters by Dennis Vicencio Blanco.