Varney. I have "the same engine" in the 4-4-0 version. Very 3-rail-able in my case - deep flanges. One day I'll...after the next dozen projects.
Above: "Would it stay on any commercial three rail track system, even with flat top rails?"
Absolutely - the 3/2 rail manufacturers use the same running rail profile (code/height may vary) regardless of the presence of a third one (this has been discussed many times). Based on its age and 3-rail track of the time, it may have run on plain Lionel tubular.
The center flanged driver would probably limit you to big curves - even 072 could be too small. Switches - that may be another matter with the big hi-rail flange ways.
Neat loco; worth resto-bashing. Varney O-parts are found on eBay, from time to time. A modern can motor could be installed, if need be.