the absolute worst experience of my life, i was told i fainted but i honestly cannot recall what happened beyond i was in a boat and started trying to jump overboard to get back to land. apparently two big guys had to keep me from jumping, and the next thing i remember is sitting on a rock and everyone telling me i am deathly pale and asking if i want a drink of water or something (no you fools i'm afraid of the water!!!).
so yes, its not likely to faint during a panic but i think its definitely an extreme possibility. kind of like, in the primal fear response if you were getting attacked by a lion or something, your body would probably make you faint in a way and go limp and stuff, kind of like playing dead so the lion loses interest in you. i dunno, its only happened to me once out of dozens of dozens of 4 years of panics... so an extreme case scenario i'd say.