I was wondering if you can audition for unpaid work in USA if you only have a tourist visa?
I really don’t know what the law requires in this case. I would think that if your visa extends long enough for you to complete the show and you are not getting paid, there wouldn’t be a problem on your side, as your participation in the play could be considered a hobby (for example, you wouldn’t need a special visa if you were going to theater camp in the States and the program culminated with performances).
A theater company may have an issue with it if they have workers comp as you probably could not be considered as working for them (I think even non-paid interns need a special training visa), but again, I’m not sure.
Sorry, wish I could be more help. Maybe other non-citizen actors will add comments. You can always contact US immigration and ask them. They have an easy to use contact form on their website.