If the vehicle is in ACC mode (just the radio works) then it will run the 12 volt battery to shutdown, no recharge, you'll need a jump to get the vehicle working again. If the vehicle is off, you can run the battery down also, no charging will activate.
If the vehicle is in Standby mode (dash active, radio active, but not drive-able), it will activate the 12 volt system when the battery gets down to 10.5 volts to charge it back up. This is the mode I use to power up my house for emergency power (so the vehicle can't be driven off by accident). But I keep the charge mode active non-stop by keeping a load of at-least 50 watts going so that the battery never tops off and it stops charging.
Finally, if the vehicle is in drive mode, the 12 volt system is active all the time until you drain the traction battery to shutdown.
Is "Standby" mode the same as what the manual refers to as "ON"? My manual only lists the following modes: ACC, ON, READY, OFF and LOCK.