Are organ donors anesthetized just in case?

Cecils column mentioned that the transplant team starts cutting away once brain death is determined, as time is of the essence.

However, do they still anesthetize the person just in case their diagnosis of brain death was wrong? They’re gonna be dead once their organs are gone, but what if they are just “locked in” and had to suffer while the team sliced them open.

Apparently anesthesia is often used on organ donors prior to and during organ procurement, but not to avoid any one-in-a-billion chance of the donor consciously feeling pain: rather, it’s to avoid damaging the procured organs with sympathetic response to the trauma of the procedure. Sez here in a CRNA nursing forum discussion: