Short form: No.
The Parking gear locks the drive tires (4 wheel drive locks all 4). It's stronger than the breaks. Those tires will not roll.
Neutral disconnects the drive tires allowing them to roll with no relation to the engine activity. This will be the easiest gear for pushing.
Other gears will also also allow pushing but with resistance. The automatic transmission will be engaged and convert your motion into rotational motion of the engine.
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