To be clear, this insurance will pay on the gray shaded "Preventable/Accidental" section.
The "Undetermined" area may see some coverage as well; best guess would be a crap shoot.
Link- National Safety Council:
https://injuryfacts.nsc.org/home-and-community/safety-topics/guns/

This graph is 2020. The latest numbers from the CDC are for 2019.
(CDC) Unintentional (Includes undetermined) Firearm Injuries: 20,814 (Estimate)
https://www.cdc.gov/injury/wisqars/nonfatal.html
(CDC) Unintentional Firearm Deaths: 486
https://www.cdc.gov/injury/wisqars/fatal.html
I guess the 2020 numbers are close.
Something from the insurance industry: https://www.iii.org/article/background-on-gun-liability
Overview
The idea that insurance can help prevent deaths from firearms often rises to the forefront of the nation’s consciousness following mass shootings.
Advocates of the idea believe that if gun owners were required to purchase insurance, the cost of the insurance would provide them an incentive to own fewer firearms and/or more carefully store the firearms they own. However, no U.S. insurance company offers separate, stand-alone gun liability coverage. In considering whether insurance is an appropriate mechanism to prevent mass shootings, it is important to note that no insurer – primary or excess – provides liability coverage for illegal acts. Looking ahead, there is very little likelihood that insurers would develop such coverage.
Excess personal liability coverage for firearms owners is available, though typically only through membership in a firearms association.
Acts that are intended or expected to cause harm are also generally excluded, though some policies will provide coverage in cases for which bodily injury or property damage results from the use of “reasonable force” by an insured to protect persons or property. “Self-defense” coverage for firearms owners is available, though rarely found.