Sadly no, unless you count a play my High School put on of The Phantom of the Opera, which for a High School, they did very well. This was ages ago. Beyond ages o.o

I've seen some on youtube, like Avenue Q. I'd love to see that one live. If you haven't heard of it, do a search on youtube. It has puppets in it lol
 
Here's one of the songs. The quality is not great because it is someone video it during one of their shows. But I find the whole show really funny. 

[youtube]6ALzUGZsOQ[/youtube]

https://www.youtube.com/watch?v=-6ALzUGZsOQ

I would love to see more shows on Broadway/live. The chance just never opens up for me. ;(