I think the answer is, "it depends". You bring up WoW and Diablo III. In both of those cases you're talking about games with hundreds or thousands of individuals working on them. While I clearly didn't work on either game, I would guess that the roles on those production were highly specialized. I would imagine that you'd probably have junior level designers who would kind of sit there and play around with a premade collection models following plans set forth by senior level designers. The senior level designers would be working on the overall plan of a given place and would be in more contact with the artists and modellers to decide when new assets might be needed. Now, I'm just conjecturing as I've never worked on a big project like that, but as a general rule the bigger the project the more specialized the roles will be.
Take, on the other hand, Bastion. According to wikipedia, there were seven people who worked on the game. One did the music and sound, one did voice acting, so then you have five people left, and they officially list two directors, two developers, and one artist. Obviously we don't know who did what really, but obviously people were doing double duty in certain areas. Maybe the artist did concept art as well as modelling. Maybe the directors got their hands dirty with the level design, or maybe they didn't and merely directed the two developers.
Point being, it really heavily depends on the scope and scale of the project. Smaller projects generally benefit from people who can fill multiple roles effectively, whereas bigger projects are going to be a lot more interested in people who are really really good at one thing.
Edit: Reread your title and saw that you specified AAA... My point stands really, but to answer your question directly, I doubt any level designers on WoW or D3 really got their hands dirty with artwork and modelling. Though at the same time I would say that it couldn't hurt to at least be able to describe what you're trying to do with a level in terms an artist can understand.