Does a Volvo S60 2007 automatically shut off when it overheats

 

Yes, as soon as the head warps badly enough to loose compression or the pistons/rings melt and damage the cylinder walls, or the engine destroys itself due to lack of lubrication.

Cars generally don't turn off if overheating or there is no oil pressure. For instance if you were in a really dangerous area where your life was at risk - would you want your car shutting off to protect itself, or want to be able to get to safety even if it meant destroying the car?

The serpentine belt powers the alternator, ac compressor and power steering pump - loosing that belt will not make the car overheat. The battery will go dead and it will be very difficult/impossible to steer at lower speeds - the water pump is driven by the timing belt.