If your MW is like my HLG-600H-54A's, the LED indicating output is active is powered from the output-wire side of whatever the output stage is. So this LED is always on as long as there is sufficient voltage on the output wire, whether that is from your battery or from the charger itself. It's not much drain, but it's there.
I don't have a 400 series, so don't know if htey have an LED or how it behaves.
The 150(?) series 12v MW I do have doesnt' have an LED, but I can hear a click inside it when powered on, so it probably has a relay (like the Satiator does) that disconnects the output from the internals when not powered by the wall.
The 600H does not click so there isn't any relay there, almost certainly.
Note that the HLG series is intended to power LEDs, not charge batteries, so there isn't any real reason they should use diodes or relays or anything else to isolate the output when unpowered...so if they do on any specific model, it's a bonus.
For my SB Cruiser trike, the MW is permanently mounted and wired to the controller side of the battery current measuring shunt (so I can measure recharged capacity, etc., when needed). There is a battery disconnect switch between that point and the battery itself, which I use whenever not riding the trike, so it doesn't drain the battery via the CA, the MW LED/etc, or the controllers.