No. I'm sorry but you have been misinformed. The oil pump of every automatic transmission is directly behind the torque converter, the hub of the torque converter directly drives the internal gear of the pump. Any time the engine is running, fluid is being moved through the pump. The torque converter does not stop in park, it moves with the engine. The same fluid pressure available in neutral is equal in park. Fluid moves through the hydraulic circuits of the transmission and cooler. In park, just like in neutral, there are no clutches being applied, therefore there is no power moving to the output shaft of the transmission. The only difference between park and neutral is that in park, the parking sprag is engaged, locking the output shaft to the transmission case. In neutral it is disengaged. There is no arguing this, this is 100% textbook FSM automatic transmission operation.
"with the selector in the NEUTRAL position, operation is nearly identical to the PARK position. The only operational difference is the park sprag has been disengaged, allowing the output shaft to move freely" That is straight out of the 44/46RE FSM.
I'm not trying to argue with or "lecture" you, but you have been misinformed, and I dont like to see false information being spread around. I do this for a living, and am just trying to help.