In case anyone else is wondering about the same thing, I'm now using query strings appended to my real url rather than non-existent paths to push to history. This achieves what I wanted, i.e. I can push states, navigate to an external page, then hit the back button and retrieve the state by listening for a popstate.
(Admittedly I am still slightly confused by the Mozilla documentation which does suggest (to me at least!) that a fake path should work.)