The automatic trans needs fluid pressure to make the torque connection; without it you're always in 'neutral'. It is true that older cars often had 'secondary' pumps at the driveshaft (my 91 Mercedes had one).
An AT can go a little while without lubrication - just as an engine can run for a little while without any oil - but it doesn't do it any good. Once you pass a certain point, it gets ruin-your-week bad. So, if the car is moving, the engine should be on.
Manual transmissions are lubricated differently - it's OK to have the engine off.
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