I’ve worked in tv/film for over 20 years dealing with famous people. I typically tune them out, but I have used them for my theater loving heart. When a Tony winner asked what I wanted as a wrap gift I definitely said tickets to a Broadway show. This gift jump started my multiple visits to NY to see more shows. LA is great for touring shows but nothing beats the intimacy of a NY theater.
JasonC3 said: "The one thing we definitely know they often do is generate a quick hit of free media exposure which, in turn, might sell some seats."
Yeah, a few weeks ago I saw The Sign in Sidney Brustein's Window and Rita Moreno, who was in the original Broadway cast, was in the audience. The press had been tipped off she'd be coming and the next day photos or video of her speaking onstage during the curtain call appeared in Page Six, Town & Country Magazine, and all the Broadway related publications.
Also, I wasn't there for this but Nicole Kidman bid $100K at a charity auction Hugh Jackman was doing after a performance of The Music Man and that went viral.
If there's some performative element to the celebrity appearance, it can help raise awareness around a show. If it's literally just someone famous was in the audience and stayed in the audience, that's probably not going to move the needle.
Going to the theater for 50 years, I've been at the same performance with many different celebrities over the years. Having a celebrity in the audience never caused me to like a show more, nor has an endorsement by a celeb ever prompted me to buy tickets. Among those I remember off the top of my head who I sat very close to:
Hillary Clinton (The History Boys)
Joan Rivers 2x (The Goat or Who is Sylvia? / Act One)
Billy Crystal (2006 revival of Company)
Elain Stritch (2011 revival of Follies)
Liza (1995 revival of Hello, Dolly!)
Steven Sondheim (off-Broadway Juno and the Paycock)
Betty Comden and Adolph Green (2001 revival of Bells Are Ringing)
There are many others, often TV actors who had popular TV shows airing at the time.