Well, I was kinda expecting the killer and the victim to be standing on said floor of reference. Not for some cirque du soleil thing to happen where you cut a person up and let him fall down from great height without him touching the floor of said platform and without you falling with him.
Though technically I'd say yes, it's possible for that head to survive a long time after having been cut off. Most people's brains don't work like a light switch. So given that it takes me on average 5 minutes to drown people, I'll assume that if the head hits the ground before those 5 minutes are over, he'll likely be alive (until the very next millisecond, where he'll be painting the surroundings.