Based on probability alone, reducing gun ownership would reduce gun deaths. Theoretically, if fewer guns are owned, there are fewer chances for death to occur as a result because there would be fewer opportunities for guns to be the source of death. This does not necessarily mean, however, the the wrong people would be prevented from obtaining guns.
Decreasing the gun ownership will reduce accidental deaths, simply by numbers. Less guns less chance of accidental death. However that is not the end all solution to the gun issue because those who want guns will still find a way to get the guns. We need more then just limited ownership.
If we reduced car ownership there should be fewer accidents from cars. If there were fewer knives there should be fewer accidents with knives.
It is worth noting that there are about 300,000,000 guns owned in the USA, but only about 600 accidental deaths involving firearms per year. There are about 250,000,000 cars owned in the USA, but about 41,000 deaths involving cars per year. I didn't determine how many of the deaths involving cars were accidents, but I'd assume it's at least 50%.
If less people had guns, it follows that there would be less accidents. Gun death accidents cannot happen when there are no guns around. The fact is that many gun owners are not properly able to handle guns or may place guns in areas accessible by people who cannot handle them well, such as children.
Almost every piece of data NOT funded by the gun lobby points to reduced risk as people disarm themselves of unnecessary firearms. I am not speaking of rifles meant for hunting but of the weapons toted around for protection.
The majority of gun accidents happen at home due to lack of foresight and irresponsibility by the gun owners themselves. Not some shadowy other that people have been fear-mongered into believing is around every corner.
While I am in favor of increased gun control for the purposes of reducing crime, I don't think we can really use the reduction of accidental deaths as one of those selling points. Stupid people are going to find a way to kill themselves even if there are no guns present.
I believe if you reduce the number of guns in circulation you can indeed reduce accidental gun deaths. Of course, when you say accidental deaths, I assume you mean people who have true accidents with their firearms. I assume you're speaking of people whose guns back fire on them or explode, or they have some other unusual problem directly related to their firearm. I honestly don't believe these incidents happen that often, so I really don't think it's an overly important goal.
If you decrease the ability for people to carry guns legally the only people who will have guns will be the criminals who have obtained their weapons illegally. Most gun owners are responsible with their weapons. The amount of accidental deaths from guns are less than that of people dying in a swimming pool each year. The criminals are the ones who need to have their guns taken away not the law abiding citizens.