Awesome question! In my experience, and in working in the past with coordinators in other regions and states, the practice here tends to vary. The bottom line is when a patient is brain dead technically there is no need for general anesthesia. However, sometimes during the moving process, the donor may become hypertensive, and gas can be administered as a quick and easy way to normalize the blood pressure.
Maintaining organ function and stable vital signs throughout the procedure is critical, so in essence anesthesia will often do their job as they know how best in order to maintain needed parameters. Monitoring ventilator settings, O2 sats etc. and adjusting accordingly is still a key role for anesthesia. On a side note, I will say I have seen paralytics given to a brain dead patient in the OR which truly was a comfort measure to the hospital staff not a need for the patient.
Thanks for reading and for the great question!