NPS-regulations state that e-bikes are prohibited where traditional bicycles are prohibited. Bicycles are not allowed on Roosevelt Island.
Whether this also means you cannot walk the bike on the island is unclear. We believe you can walk your e-bike.

Theodore Roosevelt Island - National Park Service - No Bikes Allowed - E-bike Lovers
The Superintendent Compendium and Record of Determination only refer to the prohibition of bicycling on Theodore Roosevelt Island. It is silent on the possession of a bicycle on the island.
As usual, please check the latest regulations before heading out as we do not provide legal advice on this website.
References
https://www.nps.gov/gwmp/learn/management/upload/E-Bike-ROD-GWMP-Final-9-26-19.pdf
https://www.nps.gov/gwmp/learn/management/upload/GWMP-Compendium-508-2.pdf

Gregory discovered e-biking after 20 years of overseas work as project manager for the World Bank and USAID. He writes about e-mobility and e-biking in the DMV area, and loves the outdoors (white water kayaking, hiking and biking). He lives with his wife, Janet and Queenie the cat, in Washington DC. He recently e-biked 4,685+ miles across America and raised $180,000 for a charity.
Favorite e-bike: Riese & Muller Super Charger Class 3 touring e-bike.
Dr. Gregory F. Maassen
FOUNDER E-BIKE LOVERS