you mean an actual 'behinds the scene' book, or a book that focuses on the enlisted dude that cleans the plumbing?
the first one, sure, just hit the front page of this site, there's like...40 of them. the second one....eeeh, not so easy. The SCE books are kinda like that. so are the New Frontier books, if only because they have such a large cast, though the focus is primarily on the command crew of the ships in both cases.
A good game that I played that was exactly like this was a "cd-rom adventure" that I played back in the 90's in which you're a new recruit on your first assignment, and things go sideways with the borg and Q showing up. It was a fun game if I remember correctly, I just can't remember the name of the game.
I might even have it around my office still, lol.