Accidental Death and Dismemberment Insurance would only pay for death or dismemberment due to an accident, not any natural causes.
Far more deaths occur as the result of an illness than by accident.
If you feel that your employer's life insurance amount is not sufficient for your needs, you may want to purchase the supplement life insurance policy on your own, in addition to any life insurance program you have through your job.
In addition, having your own individual life insurance plan will keep you insured in case you lose your work benefits due to your company going out of business, or you losing your job.