To date, I've yet to try. I'm using a Japanese version of Illustrator 10, so naturally can type Japanese. The problem is my productivity drops due to the Japanese menus and palettes.
I haven't used Illustrator a great deal - I've spent a lot more time in Freehand, which as yet doesn't support unicode. So I was concerned the same problem may exist in Illustrator. Glad to hear it doesn't!!
Still - that's good news, thanks. Can anyone comment on Photoshop's non-western text handling by the way?