I know airplanes and helicopters fly thanks to the same principle, the Bernoulli Principle. The wings and blades are designed so that the air travels faster across the up side than it does on the bottom side, generating an upward pressure, or lift. My question is... if the propeller rotates in reverse, does the pressure becomes downward? The distance the air has to travel from point A to B of the wing/blade is still the same so I would think that the way air moves around it do not matter. From the airplane perspective, I think this reverse rotation of the propeller would be equivalent to the airplane flying backward. So, what is the case here?
As John Rennie said, it's mainly the angle of attack. The Bernoulli effect keeps the air following the upper surface. As it is pulled down, it provides some lift. The Bernoulli effect is caused by the fluid stream carrying surrounding fluid away, leaving a low pressure zone, & effectively sucking a nearby surface onto the stream, or the stream onto it. It makes the top of the wing, or rotor do it's bit to help lift the aircraft. That's why some planes have turned up wing tips, to stop air leaking back into the low pressure zone from the side.
It depends on whether you also reverse the angle of attack via the collective pitch control. A cambered airfoil will generate lift for a positive angle down to a slight negative angle. If the angle of attack in the reverse direction is made zero or positive, the rotor will generate lift. But it will be barkingly inefficient and the chopper will just get a bit lighter, it will not take off.
Experiments with fore-aft symmetrical airfoils with rounded trailing edges, like very flat ellipses, have been tried as a route to stopped-rotor technology, but they are already too inefficient and high-drag to be practical.