I don't really know what makes something a "storygame" - given that I see it used to describe RPGs as different as Apocalypse World and Fate, I don't find it a very helpful category.
I can report, from experience, that it is possible to use AD&D and 4e D&D to run a "story now" game. And Ron Edwards has talked about using 3E D&D to run a "story now" game. 4e in my view is very robust for this purpose. AD&D is not, because both it's resolution rules and its approach to framing scenes (I say "approach to" rather than "rules for" because it's a bit loose to count as rules) are a bit unreliable as far as establishing clear stakes, and resolving them, are concerned.