Since no one's come out and said it plainly (yet), I'm going to come out and say that this is a request you would be well-advised not to make.
Put yourself in your manager's chair, and imagine an employee coming to you with this request. When I do it, the first thought that pops into my mind is wondering what the [expletive] is wrong with the person who wants to come to someone else's workplace and sit quietly. This is followed very quickly by wondering what the [expletive] is wrong with the employee making the request (because there's gotta be something wrong with someone who's with someone like that, right?), and all kinds of scenarios to try to explain or make sense of this extremely odd request come tumbling through my mind, the first one being that this could be a symptom of an extremely abusive and controlling relationship... and I wonder if maybe I ought to put in an anonymous call to the police or a battered women's hotline.
Granted, I am a bit paranoid and cynical, so maybe if you approach your boss, his first thought won't be that you're a wife-beater, but I don't see any way around him thinking you very odd for asking. And then what happens if he agrees to your request and all your coworkers see your fiancee coming in on a regular basis, and sitting quietly in corner? Sounds like a spectacular way to fast-track yourself into the position of the office weirdo and invite all kinds of gossip and the like about you and your fiancee.
And of course, were he to grant your request, what about your co-workers? I'd love to have someone I'm having sex with "sit quietly" in my office with me while I work. Wink, wink, nudge, nudge. "I swear, she won't make a sound, and I'll be a much happier employee as a result. No? Well, then why is one of my coworkers getting special treatment and being allowed to hang out with his girlfriend when he's supposed to be working?"
There's just no good way for this to turn out if you make the request, so don't make it.
The better approach would probably be for her to find a hobby, learn a new skill or visit public places, like normal people do when they don't want to sit home alone and be bored or lonely. Libraries, museums, parks, pubs/coffee shops, visiting the local tourist attractions, even something like MeetUp or volunteer work would be normal, healthy reactions to not wanting to be home alone, as opposed to this idea, which at best will only result in people thinking you two are weird, at best.