Being someone who has woken up during the middle of a few different surgeries, and have had quite a few "out-patient" procedures where the anesthesia didn't take properly (but left me in a relatively shtoopified state) . . . I can fully understand what the guy musta gone through . . .
. . . and yeah, doctors do sometimes make the decision to continue with a procedure. I once had oral surgery where 4 molars were being removed, and was put under (thanks to how I tend to brush off local anesthetic) and I woke up during the procedure, I remember being in hellatious pain, then blacking out again. The surgeon approached me in recovery afterwards, and apologized for it, but stated they had already given me enough anesthetic to sedate 10 grown men, and any further medicine was out of the question.