Accidental death is usually covered by a life insurance policy as an insured cause of death.
However, the coroner/autopsy would probably need to determine that the death was a result of an accidental gunshot.
If it was determined death was a result of suicide, the suicide clause would kick-in and exclude payment of the policy if the insured only owned the life insurance for less than 2 years, 1 year in Colorado.
But, if it is determined to be an accidental death, the life insurance policy would probably pay out the death benefit to the beneficiary of the life insurance.