Could you imagine if radios or other car electronics were real easy to damage by putting 9 volts across them? Every winter there would be a rash of dead electronics. How many here have cranked that the starter on a cold winter morning and seen the lights dim, thats your voltage dropping. If you crank a little too long you can get to 9 volts, pretty easy, give it a try.
Now I don't know if a 9 volt battery has enough voltage to save the memory in every case, but I would guess so, semiconductor memory is very tolerant to voltage. But that little 9 volt battery is not going to damage anything, especially a parasitic junction in power MOSFET. You would have to try very hard to make a circuit that would work reliably on a nominal 12 car battery but be damaged by a 9 volt transitor battery.
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