I wonder if this is limited to improvisational theater or if something like a roleplaying game, where the person has to act out a role with no script, can help as well. I would think that they get to perform the same sort of social interactions and while still being "low cost".
I'm guessing that the best script for people with some kind of anxiety is: acting that you simply don't care. That way, you don't look stupid, just a little uncooperative or disinterested. From there you can build on confidence, thus keeping your head from overflowing with negative thoughts, and actually making a more interesting performance.
