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.

I've done cultures on agar agar and mycelium definitely does have a distinctive smell. To me it's reminiscent to the damp smell of a concrete basement, though less stale and unpleasant.

Chanterelles smell great. I would wear something that smelled like that.

Pine mushrooms, not so much.