I don't know, trial and error is the only way to know for sure, there is a very good book ( Mushrooms Cultivation, Nutritional Value, Medicinal Effect, and Environmental Impact ) that I happened across at the university I use to attend and is what I have quoted form above, parts of it are available at
Google Books but most of the good bits are missing.
They do talk about growing them in sterile mediums with success and even without a substate and just liquid.
"it is best to use compost to feed the mushrooms because they need to gather
nutrients from a source because they can’t make their own food since they have no chlorophyll."
from that book "The composting process in which substrates, such as straw and manure, are wetted and acted on
by naturally occurring bacteria, Actinomycetes and fungi, involves thermophilic microorganisms.
These microorganisms break down the complex compounds of the substrate into simpler compounds,
such as glucose, which can be taken in by the mushroom mycelium."
supply them with glucose direct all the other elements can be supplied as a salt as far as I can tell.
Anyway its not one of my high priorities at the moment, will buy some spawns and see how we go. Think I will just flag the flood and drain and just use passive wick system, put it in my closet and see what happens.