To be sure, the LED indicator would have to be in a secondary SERIES path to acurately determine current flow to the battery.
The way its currently configured, you are only assured of verifing the charger is engaged, not the batteries.
A transitor based current sensor with LED indicator, would tell if the batteries are truely being charged or the tank being supplied power.
All in all, they really would not be needed when the switch can show CHARGE and ON positions.