Broadway61004 said: "It doesn't hurt them at the box office though. I agree it may just delay the inevitable and end up costing the production more money, but speaking strictly in terms of box office, they almost assuredly sold more tickets this week than they would have had they gotten shut out of the Tony noms."
What you say is the absolute truth. As a producer, you want to sell every ticket you can, and nominations sell some number of tickets, even if that number is small. Good producers respect every sale.
This reminds me of a time I was at a cocktail party and heard Gerry Schoenfeld sell two tickets to a failing show the Shuberts were producing to a man who didn't know what hit him.
If I hadn't known better, I would have thought Gerry needed lunch money.