If I am not seeing a particular show that day, but was interested in purchasing something from inside the show (ie..mug), would they let me in to buy the item then I could leave like before during intermission or after the show ?
Yes. (Especially if there is a merchandise person in the lobby.) However, you are less worrisome if you do it at the end so then the staff doesn't have to worry about whether you are trying to sneak in.
If we're not having fun, then why are we doing it?
These are DISCUSSION boards, not mutual admiration boards. Discussion only occurs when we are willing to hear what others are thinking, regardless of whether it is alignment to our own thoughts.
It should not be a problem at all. Just tell the ticket taker or House Manager that you'd like to buy something from the Merch booth. Usually they don't have a problem with that. And a lot of times, things like t-shirts and mugs are more expensive at the souvenir stores and even online unless a show has closed.
I've asked to be let in to buy merchandise right after a show has let out before and it hasn't been a problem. I believe Trip to Bountiful has a counter in the upper lobby so I can't imagine it being an issue.
I was told that One Shubert Alley closed earlier this year. I hope that was misinformation because I was super bummed, but since I don't live in NYC I haven't confirmed the info.