The mushroom smell isn't from either the substrate or respiration. That distinct odor is 1-octen-3-ol. Biochemists call it "mushroom alcohol." It's caused by enzymatic breakdown of their cell walls, and it thought to be related to signalling.

I doubt it would be strongly present here. The article says the mycelium are close to dormant.

You can actually purchase mushroom alcohol commercially as a food additive.