That sounds convincing and most of the equipment can often stand variance of between 8 - 18V, so even if it was a bit under 12V it'll still be okay....I think
Now, the only other thing I was thinking was when does the relay give up and open? What am I talking about:
Your backup battery is the power that is being used to close the relay (when the master switch is turned on). When all is working the aircraft power will charge the backup battery and all is good. Now imagine a power failure. Your backup battery will power the essential bus but when the backup battery voltage gets below XXX volts then it won't be able to hold the relay closed and it will open, thereby cutting the backup battery power to the Ess bus.
Do you happen to know what the XXX voltage is because Google hasn't let me know yet and Siri just wonders what the heck I'm talking about
Edited to add: let's pretend you haven't got the essential bus switch, which connects your main battery to the bus.
Edited edited: It would seem that the relay may stay closed until about 7V, by which time most of the gear it's powering would have gone to sleep. Apparently a relay needs a higher voltage to close the relay than to keep it closed (and all sorts of stuff about temperatures etc but that was the long and the short of it).