The Hot Battery Bus (HBB) is always hot. The 'BAT' switch controls the Battery Bus connection to the HBB and therefore its state (energized or not).
To answer genbb's question, upon failure of the battery charger, the BB and HBB loads will be powered from the battery. This will slowly discharge. Not as rapidly as it would when powering the standby systems (30 minute design capacity, more with the hydraulic generator) but over the course of several hours. This assumes that main generator power remains to support all other electrical loads. The rate at which the battery will be depleted depends on the BB/HBB loads. I don't know off the top of my head, but assume 4 Amps for the purpose of discussion. This would deplete the battery in approximately 10 hours.
Absent a QRH procedure or company policy, its a juudgement call whether to divert or not.
