I think maybe you are misunderstanding the role of the switch in that the BMS is hard wired into the battery - the switch merely activates the electronic switching components (aka FET's) in the BMS to 'connect' the battery voltage to the output terminals of the battery pack (which is why the switch needs to be in the 'off' position when removing/installing the battery pack into its holder - this prevents sparking between the battery pack terminals and the battery pack casing terminals).
The switch position, on or off, has no effect on the charging of the battery nor in the balancing function - as has already been said, if the charger light goes from green to red, be confident that the battery is being charged.
So the BMS is always taking some power from the battery but it is really small with the switch off and a bit more so with the switch on, but still small.
Do a google search on something like '10s BMS schematic' to get a better understanding of these things.