Don Durito
Hero
I'm as sure that it could be done as I'm as sure as I wouldn't want to play it.I taught a 6 year old to run 4e.
With enough random die tables, you could probably run a very basic game of D&D with no DM.
There'd almost certainly be something more enjoyable I could do - like root canal perhaps.
Edit: I've played those board games that are dungeoncrawlers. I know some people like them but to me they feel like being stuck in a D&D combat that never ends with a GM who will shut you down immediately if you try to do anything creative.