It might happen to your car, but it won't be as catastrophic as the error messages say. I actually had even more errors than that when my 12v died (including "Vehicle may shut down unexpectedly"), and I still managed to make 2 stops before going to the Tesla Service Center to have it replaced.
The reason that happens is that batteries behave strangely when they go bad, so that most electronic sensors can't fully zero in on what the problem is. The voltage drops, but then sometimes they actually intermittently short internally or behave like a resistor on the 12 volt bus. Then you get strange errors like the ones you saw - the extra ones I got might have been because it was shorting internally, and was cutting off 12 volts entirely from time to time.