Powering the BCM is OK but there are number of caveats and gotcha's.
1) Why bother and just use an OBDIIC&C or Mike's SOC reset device to set the soc to 19 bars when you come out to the car in the morning after a grid charge. That takes about ten seconds.
2) If you decide to power the BCM overnight you must power it up before
you turn on the charger or it will not count the current correctly.
3) Powering the BCM independently of the rest of the car electrics is best done by adding some diodes to it's 12v power feed wires and connecting an approx 1A 12v power supply on the BCM side of those diodes. Otherwise you end up powering up the whole car/ignition system. The car consumes quite a bit of 12v power when sat with just the ignition on (around 200w estimate) as we all know from how fast the 12V battery dies when the dc-dc converter is not working.
The IMA will also likely be energised and the DC-DC converter
which means you waste a lot of the power in those systems as well.
I suggest someone uses a smart plug to count the KWH consumed by leaving the car turned on all night versus
the BCM powered alone and versus
just powering the grid charger and reseting the soc in the morning.