Under most conditions, the G-V is always flown with the autopilot on. It's not impossible/unheard of to hand-fly the jet in cruise, but really unnecessary, and certainly not normal.
It's not very realistic to expect a pilot to be hand-flying the jet, with the other pilot incapacitated, and decide to just turn on the autopilot and leave the cockpit. At the minimum, the pilot would have a flight attendant come up front to at least monitor the incapacitated pilot and the radios, while the autopilot was on. But even that is a bit of a stretch. It would have to be something REALLY drastic/hilariously implausible to get the pilot flying to just leave the cockpit unattended. Zombies onboard/snakes on a plane/aliens/etc.
In the real world, having an incapacitated pilot would lead the pilot flying to declare an emergency and initiate a descent to a suitable airfield with some sort of medical facility. The only scenario I can think of where they would just keep on cruising would be over the middle of an ocean, middle of nowhere Africa, etc.
The autopilot will turn off for a few reasons... mostly having to do with a yaw damper failure, some fault in one of the various computers, etc. There is an audible warning that the autopilot has been disconnected, but it wouldn't be audible to someone beyond about 3-5 feet from the cockpit.
Feel free to PM me or the others if you want more help. At least you're asking questions and doing your homework... most things aviation-related in the entertainment industry are hilariously inaccurate.