I think they can affect each other, but I don't think it has to be competition. To take your example again, the woman who realises her new lover does things she likes could tell the first man about that thing she realised she liked, and as a result her relationship with the second man improved her sex life with the first one.
I think you can learn to appreciate people better too, when they're different you can see how they are unique better and love them for how unique they are.
I think anything can influence your relationships, because things that influence you will do so in more than one area. So I do believe one relationship can affect another, but I also believe that a friendship can affect a romantic relationship and vice-versa, and I absolutely don't mean it in a bad way.
I don't think it would work quite the way you say, though. The hinge wouldn't do something that isn't enjoyable, whether there is another man or not. And if the thing is enjoyable, then she'll want to keep doing it with both. It's like... I don't know, say you love pasta, but you also like rice, you're not going to eat pasta all the time and stop having rice.
You might say "yes, but before there was only rice..." but that's not true, because the time you're spending with a lover, you could be spending it with a friend, or alone, etc.
I'm not sure if I'm making much sense here.