Can a completely drained battery be recharged via ground power on an airliner like the B737?
My one experience with this was in a 737-300 that had the battery charger die, and the battery depleted while in flight.  The Battery Bus was still powered by TR3, but the Hot Battery Bus died (interestingly, not a scenario I'd ever seen in the simulator).  We got to the gate &amp; couldn't start the APU and couldn't connect ground power, so when we shut down both engines, we immediately had &quot;one blue light&quot; -- i.e. ground power is plugged in &amp; available, but NOTHING else -- dark airplane.
I don't recall how longer after that it was, but we eventually were able to connect ground power, probably to the ground service bus first.  Then, with the ground service bus powered, the battery would recharge.  I don't recall if we were able to get anything beyond the ground service bus powered after that.  (Presumably, if the battery recharged enough, we could have gone back to normal routines.)
As a practical matter, though, our maintenance does exactly as John K mentioned: if the battery has been depleted, it gets replaced.  How much of that is a matter of what happens during charging, and how much of that is concern about damage to the battery itself, I don't know, but in practice they won't use the aircraft's battery charger in the manner suggested in the OP.  (The battery charger brings it back up to full charge after things like starting the APU or running on battery power for the time between initial power-up and when APU or ground power are connected -- but that's a long way from being fully depleted.)