If the aforementioned vehicle has a VW DSG transmission, the clutches default to "open" (uncoupled) and in a key-off situation, that's what happens. YES, this is the reverse of what happens with a manual-transmission clutch. The VW DSG clutches require active energisation in order to engage. Key-off? No torque transmitted. No bump-start for you. It will not command the clutches to engage if you attempt to bump-start the car.
Re auto trans being used for bump starting ... Keep in mind that they are not only reliant upon the torque converter being filled with oil but they are also reliant upon the correct internal multi-plate clutches being supplied with hydraulic pressure in order to transmit any torque, whether due to the engine driving or in over-run coasting (or in an attempt to bump-start).
If you go back to the dawn of hydraulic-controlled automatic transmissions, up to the early 1960s, they had a front pump driven by the engine and a rear pump driven by the drive shaft, expressly to permit bump-starting. You shifted to "drive" (no electronic controls in those days), had someone push the car, the rear pump developed pressure which engaged the clutches and then hopefully back-drove the engine to start it. It would have to be pushed fast enough for the torque converter (or, originally, fluid coupling) to transmit enough torque to get over that first compression stroke ...
In the mid sixties, the rear pump was deleted, and that was the end of bump-starting. If the engine is not running, the pump is not running, therefore there is no hydraulic pressure to engage the clutches. Doesn't matter what gear range was selected, doesn't matter how fast you spin the drive shaft in an attempt to back-drive and bump start. Pump not running -> no pressure -> no clutches engaged -> nothing happens.
Now, add to that the electronic controls, which also default to "off" in a key-off situation.
The thing that I don't know, is on a vehicle that has complete automation (switching the key off doesn't actually key-off anything), if you commanded engine-stop while rolling forward, is whether it would detect this and leave the transmission coupled in the interest of keeping the power steering and power brakes working, or whether it would simply cut all solenoid power to the transmission, in which case all solenoids go off, and all clutches disengage.
