This actually was done before, a couple years ago. It was pretty small-time, attracted 25 people or so, was like a half hour play, but was really fun to watch.
I'd love to see a full production (or at least the semblance of a full production) done in AO.
But an entire Shakespeare play? I don't think you could find enough players willing to dedicate that kind of time and energy to rehearsal and prep. Perhaps a minified version of one.
(yes, I could've posted this on the thread, but I'm still on self-imposed ban on AO forums)