Maybe? I'd need compelling reason to use that format though. I used to MU* a lot too, and loved the format for rules-driven games to be played by a large number of people at once. A MU* could totally be set up to do what you're talking about, and a couple of decades ago it would have been the ideal platform for this sort of thing.
But the rules light nature of Apocalypse World, with moves providing choices and campaign specific custom moves, limits the usefulness of a MU* environment. I have a hard time seeing it offering much more than communication (via text), a dice roller, character sheet management, and possibly a session log.
So, why would I use this over a virtual tabletop, like Roll20, which is already overkill mechanically? The VTT usually offers the dice rolling and session logging. Communication is usually done via voice (and sometimes video), and character sheets are usually intuitive form fields that don't require commands to edit. Most also offer image/file sharing/editing as well.