Since the great majority of Broadway shows close at a loss, this "fund" doesn't sound like a likely vehicle to choose if any investors are hoping for a profit. And it seems to me that if someone is willing to throw some money away, they're going to want to choose the show upon which they'll lose that money.
In other words, how many people do you think there are who would happily give $2,000 to someone and say "invest this in any show you like?"
Also, if this "fund" aims to invest in 5-6 Broadway shows, and hopes to be a significant investor in all of them, it would need at least 2,500 participants, I imagine. That's a lot of chickens to pluck.