For the record, I just experimented with it.
A little essence of the coconut milk with some Emmental and cream cheese, was not a bad experience. It was interesting, if not a little bit odd - could be improved somehow, but it's not screaming at me to be explored.
Once I also added some of the other ingredients, namely the beef stock and the flavours from the mushrooms, peppers and garlic. There was a distinct oddness to the flavour, and I attribute that to the coconut milk.
So in short. I won't be repeating this adventure again.