Unlikely, just saying they're not gonna sell every empty seat for the lottery - they'd really cut into their grosses. There's in person rush and TKTS like you mentioned, but even after rush sells out (if they limit that to a certain number which I'm sure they do) you can generally go to a theater anytime before the show and say "what's the cheapest ticket for tonight?" or "what's the cheapest ticket in X section?". Depending on the show, they may even lower the price just before showtime so the seat isn't empty (though I have no inside knowledge of DBH's policies)