The one near the hatch is the most likely to stay on, if any. That's probably where you'd try to hook up the compressor if you had a flat or low tire.
Keep in mind that all of the electronics are run via the 12vdc circuits, but that small battery is only kept charged while actually hooked to external power, or while in the ready state. If the 12vdc battery gets flat, even if the main battery is full, you may be stuck, so you want to avoid a big load. I seem to remember the 12v outlets are limited to 120W, so watch what you plug into them, too.
There's an emergency feature that will charge the 12vdc battery if it is too low to allow 'normal' EVSE charging, which requires the computers to manage things...it will bring that battery up to a high enough charge, and then will switch to the normal charge process to then recharge the main batteries. Depending on how flat that 12vdc battery is, it could lengthen the overall recharging time by a fair amount.