Does a helicopter battery drain when it is "off" but attached to a battery hot bus?
This is the same setup as a typical automotive/car/truck electrical system.
You have a Switched bus, that's only on when the key is on Acc/On. The Key Ignition switch enables a power relay to power most of the car, like radio, windows, AC, and further for the Starter Motor. High drain devices that only need to be on if the user is already in the car.
Then you have an Always On bus. These are directly connected to the battery, without any relay. Typically, this will be alarm systems, keyless entry, door locks, some headlights, some cigarette/power outlets, clocks, the ODB-2 or CAN-Bus system, some lights. Most of these are very low current draw systems, or not constantly active without user interaction (roof light, headlights, motorized windows, electronic locks).
Yes, the battery is slowly draining with the Always On bus, it's just designed to be very low draw, with active use/recharging.
This is why you are typically expected to use the car on the regular, to prevent this from even being notice. Letting a car sit for a week isn't normally an issue, but Long term sitting/non-use, like weeks (or a month for new/good batteries), will drain it enough to need a jump. Long term storage recommendations are to disconnect the battery completely, or use a battery tender.
This is also why leaving the headlights or map lights on will drain the car overnight. These are Always On/Hot systems. Same for any Always On cigarette outlets with a cell phone charger or similar.