Not quite sure.Mushrooms are not plants by definition.
Obviously they must require some oxygen in order to grow, but blowing them with a fan could cause the cakes or casings to prematurely dry out, or introduce some airborne contaminant.
It sounds like a possible way to make the mushrooms grow "fatter" but then again that may jsut be a waste of the cakes moisture as well, since you will dry them eventally anyway.
I've found that cakes that I injected water into created some huge fat asses, but when dried they shrink to less than half the size they were fresh.
Maybe someone with more mycology background can help further?