Unlikely that any NYC J3s (or other engines, for that matter) had access through the tenders. The J3 tenders were often swapped; for example, the original 12-wheel tenders were swapped for the 4-10-0 PT (pedestal type, or centipede) tenders, and sometimes an engine went through several tenders during its career (e.g. I have seen a photo of a streamlined J3 with a non-streamlined PT tender, which would have been at least its third tender). I have never seen a photo or film of an NYC tender from the rear showing any kind of doorway. Although a limited like the 20th Century had few stops for passengers between Chicago and New York, and could take on water from track pans, the train must have at least stopped at division points for crew change.
Dr. R. C. Leonard, "Richard Leonard's Rail Archive" (
http://www.railarchive.net/ )