Yes it needed DOS because pre-3.11 Windows versions actually used the DOS kernel for all file access. When 32-bit file access was introduced in WfW 3.11, that was no longer true-but it was an optional feature you could turn off. In all pre-NT Windows versions, Windows is deeply integrated with DOS, even though in 9x/Me that integration is largely for backward compatibility and mostly unused when running 32-bit apps - but still so deeply ingrained into the system that it can’t work without it.
IIRC, Microsoft tried to sell the same stripped down single-app-only Windows version to other vendors, but found few takers. The cut-down Windows 3.x version used by Windows 95 Setup is essentially the 3.x version of the same thing. Digital Research likewise offered a single app version of their GEM GUI to ISVs, and that saw somewhat greater uptake.