Starship running on mushrooms? Yeah, why not
The mushrooms are some omnipresent thing connecting all space and time together and giving some special super powers somehow? The force stolen you have. Integration of science fantasy into science fiction unasked for was.
The Q know about the mycelial network, likely because they created it for their own purposes. That's how they can seem to transport anywhere in the universe. Quinn essentially admitted as much when he said that their "magic" is simply very advanced technology. A mycelial network permeating subspace would be right up their alley.