It does indeed, it actually checks battery voltage before programming. It shows mine as 13.8V with my power supply, linked above.I am not sure if battery chargers cut it. SDD needs 12.5V before it kicks into updates
Sounds like your battery charger isn't working correctly, as a PB battery isn't charged until it's voltage has reached 13.6V, which wouldn't happen if the charger only reached 11.8V.even my heavy duty battery charger only puts out 11.8V going by SDD