It will run it's course, but that could be years. I have a friend who had an A, his W wanted to work things out but he was totally fogged out so they ended up D. He is now married to his affair partner and they had a baby last year. Just saying, they don't always "run the course" and peter out.
Exposing the A is not guaranteed to end it, but it sure does increase the likelihood because A's thrive in secrecy.
Some people don't want to expose because their WAS will feel too much damage will be done and not want to come back. Others don't want extra people involved in their M. Still others are ashamed and embarrassed by their sitch.
I don't fall into any of these categories. If BF was going to have an A then I had no problem telling people why we broke up. I was not going to let him tell family and friends some BS story and make it seem like it was my fault or no one's fault. So yes, I did tell my parents, his parents, and both sets of friends.
Did it complicate matters? Yes, to some degree. I do feel like my friends and family disapprove of me taking him back and I worry that if things don't work out they won't be supportive like they were when I kicked him out. Did it make BF hesitate to come back? Nope. He knows I told everyone and he knows that if he wants to get back into my friends' and family's good graces that's up to him to do.
If I had it to do over I would perhaps try to limit exposure to my closest friends. But then again, I'm an oversharer by nature so it would probably be about the same.
Do what works best in your sitch, but I'm definitely pro-exposure.
If you love somebody, set them free. http://tinyurl.com/2empx2g