Emergency Telework Act of 2020 This bill requires each federal agency (executive, legislative, and judicial) to allow eligible employees to telework full-time during the public health emergency declared on January 31, 2020, relating to COVID-19 (i.e., coronavirus disease 2019). An employee is considered eligible if the employee has not received specified disciplinary action and is otherwise determined eligible by the agency. In the event the public health emergency is renewed, the bill's requirements continue to apply if the Department of Health and Human Services (HHS), in coordination with the Office of Personnel Management (OPM), determines the requirements would reduce the spread of COVID-19. If the requirements no longer apply, agencies may still allow high-risk employees or employees at certain work sites to telework full-time during the renewal period. Additionally, OPM must, in coordination with HHS, develop an expansive telework policy for use in future outbreaks of infectious diseases.