Folks from Wall Street and Utah and Japan do not follow the message boards. They buy based on word of mouth ("My co-worker loved it!"), name recognition ("I love Cyndi Lauper!") and critics' quotes they see in the papers and on the marquis ("The best musical of this century!"). The last will never be replaced by says "I love anything with Kelli O'Hara!"
I think there are a lot of variables that go into the success or failure of a production, so it's hard to give a definite answer. However I would lean towards no, since I'd be willing to bet that most people who attend Broadway shows don't read reviews and rely more on word of mouth.
"You drank a charm to kill John Proctor's wife! You drank a charm to kill Goody Proctor!" - Betty Parris to Abigail Williams in Arthur Miller's The Crucible
Often people just adopt the opinion of reviewers. It can harshly effect people's opinion. I know that I personally don't care much for reviews because most critics see things I honestly couldn't care less about
The article does not distinguish between the impact of reviews of plays v. musicals, but I believe that the Broadway League has published data on the question. If my memory is correct, positive reviews are far more important to the success of plays, and bad reviews of plays will basically kill them. On the other hand, word of mouth is what is critical to the success of a musical. If a musical gets very good word of mouth, it can overcome poor reviews. I guess the best example I can think of now would be Wicked.
CZJ at opening night party for A Little Night Music, Dec 13, 2009.
I thought "Wicked" got mixed reviews. It was nominated for Best Musical and lost in what most people considered a major upset so IMO it was not entirely word of mouth that made "Wicked" the huge hit.
The only review I care about is my own. There were lot of shows that were praised by critics and I found myself getting bored only 10 minutes after the curtain goes up. Sorry but I am also a person who couldn't get into both Rent and Wicked.