“Having decent alternators means that the battery charges quickly - unlike those on some conventional aeroplanes where there is insufficient alternator output at idle to prevent battery depletion.”
When I designed my electrical system I had to read a lot of text books. I will look it up tonight, but the rate a lead acid battery will charge, using standard charging circuitry, is very slow. I think, from flat, you would need hours, not minutes. An interesting point to note here is that when a power load is drawing a high current from the battery, the voltage will drop. This may mean that the battery needs to be somewhere near 50% charged to avoid a low voltage situation.
You have no reliable way to know the charge state of the battery you are about to rely on to avoid a nasty surprise.
Rod1