According to the War Paint thread on this board, there's no stage door at that theater. Patti and Christine both exit through a private door (with a barricade) into private cars and haven't interacted with the audience after the show.
"Contentment, it seems, simply happens. It appears accompanied by no bravos and no tears."
Random tidbit, across the street from the Goodman's entrance (where War Paint is currently) is the alleyway for Chicago's Oriental Theatre where Oriental's stagedoor is located. That alleyway is one of the most haunted alleys in the country. Before the Oriental, the Iroquois Theatre stood there. During one of the first performances at the Iroquois, the theater burned down and killed ~600 people in the theater. That alleyway is where hundreds of people jumped out doors (where there were supposed to be fire escapes) and windows to their death.
That alleyway is super spooky and I NEVER hang around that stage door, not even for the Spongebob cast. Not to mention, John Wayne Gacy supposedly used to pick up boys in that alleyway too. I know, I know super off-topic, but I thought maybe a few of you would be interested.