Data from history and the world doesn't bear that out at all.
Firearm ownership rises and falls, much like crime rates. Initially there were militia requirements in America which required all able bodied men to have a firearm. If they couldn't afford one, one was often provided. Firearm ownership was fairly high, but crime/murder rates were low (from what little information has been gathered). In the 1840s some information showed that while firearm saturation was down sharply, crime and murder rates were up. Post civil war saw the biggest ever increase in firearm ownership, but crime and murder rates declined sharply in most areas. Much better record keeping began after WWII, and showed low firearm ownership, and low murder rates. Murder and crime then increased substantially along with firearm ownership, only to see crime and murder fall away back almost to the 1950s levels while firearm ownership remains 5 times the previous per capita numbers.
Many countries with similar firearm ownership have near zero crime, while many nations with few if any guns have excessive crime. This again demonstrates that firearm saturation is unrelated to crime statistics (other than the fact that with successful near total controls on firearms those specific crimes will be far less obviously).