I have no personal basis for answering this, but I do have experience from others. I read the question, and since it's a slow day here in the kitchen, chatted up my fellow cooking types. General consensus, with the exception of 1- No, don't do it. Out of the 5 guys talking, 4 of them were in a situation similar. They thought, along with their respective spouses/girlfriends, that it would be awesome, like a porn flick where everything looks and feels cool and awesome. Apparently it was not. It was either awkward, people's feelings were hurt due to jealousy that they were not aware existed beforehand, and in the case of 1 open-minded cook and his apparently very open-minded wife, a divorce came out of it because the other woman had feelings that she apparently said were under control. The woman interfered so much by calling and basically turning into a crazy person that his wife couldn't take it and bailed.
Now, the one exception. My prep cook said he had a threesome about a year ago, but it was his girlfriend and a woman they met at a club. He said it was awesome, but also that he knew he would never see the other woman again, so he went for it.
Take from this what you will. I say do what you want, I don't know all the details of you, your fiance, or the friend. If you're sure nothing bad will caome of it, do it and I'll raise a glass to you. If you decide not to, I will raise a glass regardless.