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I've only heard of one TTM "backstage pass" so to say...and it was from somone from a Broadway show. I don't recall the show, or the performer, but the person who I was talking to said they didn't write to the star of the show, but someone who could still be considered a "featured actor". They wrote them a letter saying how much they liked them and had seen the show 14 times (not a lie!). They said that next time they were up to the show, e-mail him before-hand and he'd take him back afterwards.
Also, sometimes at the stage door for stage shows, if you're extra friendly towards the cast and you go more than once (so strange I know) they might remember you and ask if yo uwant to go backstage. So always be friendly with the stars!