The supervisor chip will not see the 12V from the car battery, or the voltage from any NiMH battery pack.

The supervisor chip will only look at the output from the 5V regulator. It will not release the reset line until a fixed time after the 5V voltage has stabilized. And it will reactivate the reset line instantly if the 5V drops below a threshold.

As noted, some processors has brownout functionality internally, i.e. that they will stop the processor when the voltage drops. Some of the internal brownout solutions can work in two-step mode. At one voltage level, they generate a warning to the processor: Quickly save any pending work - power is dropping. At a second voltage level, they put the chip in reset state.

If using a chip with internal reset + brownout handling - do ask around or spend some time with Google to see if any people have had problems with the logic. There are a couple of processors that does not have as good reset/brownout logic as the manufacturer claims.

Note that depending on your needs, you will also be able to find 3.3V processors and 3.3V supervisor chips. Just remember that the supervisor chip must have the same polarity of the reset signal as your processor. Most processors have active low reset, so most supervisor chips have an active low output. When using a 8051 with active high reset, you obviously must make sure that the supervisor chip produces an active high reset signal.