Unnecessary, the transfer case pump is on the main shaft and fluid is circulated as the driveshaft turns.
And running the engine in park or neutral, without driving, does nothing to circulate the transfer case fluid. The vehicle has to be in motion to drive the transfer case pump.
Manual transmission in any gear, automatic in park. Reason is, you will burn up the transmission if it's left in neutral and turned by the rest of the drivetrain. This info is also in the owner's manual.
During braking it will provide slight downward force on the rear of the tow vehicle, improving handling and braking. I've towed several ways and it makes a difference.