The charge monitoring system should not act as a significant continual drain the battery.
Define 'significant'. While it is possible to build a microcontroller-based system that has sub-milliampere current demands, I'm not certain of the technology of the monitoring equipment inside the battery. Its possible that on the shelf it runs in a sleep mode, with a few tens of microamperes load. But when installed and communicating with the charging system and other airplane equipment, it draws far more.
All other 'parasitic loads' would surely be met by the generators that would be running if the battery is being or has been charged.
On the 767 and 747-400 there are a few loads powered off the battery bus at all times when the bus is energized. Although this didn't amount to more than a few amps, it was supplied during normal operations by the battery charger's T-R (constant voltage) mode. These sorts of loads together with the battery internals are what I consider to be parasitic. That is, always connected (unless the bus is switched off) and not switched over to other sources.
This bus topology may have been carried over to the 787 from models with NiCd batteries, where floating the battery was a non-issue.