I have had the same idea, as I'm facing maybe oh 20 or 120 acres of buckthorn and wondering what to do with it.
One concern I have is that buckthorn is allelopathic (makes soil toxic to amphibians and plants that are not buckthorn) and is also cathartic, ie it makes birds
poop a lot ,which is how the seeds are so quickly dispersed. I have a house rabbit and I have read not to feed buckthorn twigs to
rabbits for this reason.
So I am concerned that shrooms grown on buckthorn may be harmful to consume. I will probably do some trials anyway, and update this post in a year or two after I have learned something.