Yes, I believe an accidental overdose is just that, an accidental death, and would be covered under your life insurance policy as a covered cause of death.

I would however expect a full investigation to rule out suicide as a cause of death if the life insurance policy is less than two years In Force.

If your life insurance coverage has been in place for more than two years, whether your death is accidental or intentional, the claim should be paid in a timely manner to your beneficiary.