This is an i-zombie at the behavioral level, so it isn't entirely unrelated. You're right about the complete-physical-description level, which is the philosophers' favorite. The authors do point out that the poorly anesthetized are not i-zombies at the functional level, which also implies that they're not, at the complete physical description level.
What puzzles me is why they appear to favor functionalism for (e.g.) pain, over type-identity theory. None of their main points depend on it. And the supposed "advantage" of functionalism, that it affirms the mental as the source of behavior causation, applies equally to type-identity.
I offer for LW's consideration the interesting 2008 paper "Inverse zombies, anesthesia awareness, and the hard problem of unconsciousness" (Mashour & LaRock; NCBI); the abstract:
3. Inverse zombies
4. Anesthesia awareness and anesthetic depth
5. Philosophical implications of i-zombies
6. The hard problem of unconsciousness
The awareness rate is chilling. One wonders whether surgery rates would be significantly affected in everyone was aware of this; it's like that utilitarian puzzler 'how much would I have to pay you to torture you with amnesia afterwards?' but in real life.
Further reading
References
102(5), 937–947.