On the topic of if the 12V battery is maintained while plugged in, I always assumed it was at all times while plugged in even after the HVB was done charging.
Now I came across this detailed OBD operations document a while back that I recall had some details regarding the overall hybrid system operation. Had to actually dig for this one. Going to leave it here and keep a bookmark for the future:
The good bits on this topic start around page 145 and the key bits seem to be around the first 2 full paragraphs on page 148:
During high voltage charging the BECM commands the outside air (OSA) duct mode door actuator to open. This
allows outside air to be pulled into the High Voltage Battery pack to cool SOBDM. The BECM monitors the mode
door position and motor circuits and sets a DTC if a fault is detected. The SOBDM monitors its internal temperature
and commands the charger cooling fan speed accordingly to prevent overheating. When high-voltage charging is
complete the BECM charging state HEV HS-CAN message switches from charging to charging complete and
opens the high voltage charge contactors. The SOBDM continues to charge the 12V battery while AC input is
present except when commanded off by the SOBDMC.
During high 12V electrical loads or if the ignition is turned on while the vehicle is plugged in the main DC to DC
Converter Control Module is enabled to charge the 12V battery. If this occurs, the SOBDM disables its low-voltage
support and no longer charges the 12V battery. However, it continues charging the high voltage battery. The
SOBDM shuts down if the PCM no longer requests low-voltage support and the BECM status is charge complete.
Thought to me it seems the two paragraphs contradict each other on the matter of the LV charging state after HVB charging has finished. I think just doing some direct testing is the best method in this case to verify.
I may have to do some testing later tonight when mine finishes charging and see what I can find.