Emergency Advance Refill Notification Act of 2020 This bill requires private health insurance plans that cover prescription drugs to notify plan holders about the plan's policy concerning advance drug refills in response to a national or public health emergency. Specifically, the plan must notify plan holders in emergency areas whether the plan is waiving time limits on authorized prescription refills and, if so, the process for obtaining an early refill. Plans must issue such notification within five days of an emergency being declared. Concerning the public health emergency declared in response to COVID-19 (i.e., coronavirus disease 2019), a plan must provide initial notification of its waiver policy not later than five days after this bill is enacted.