Aside from the fact you would disintegrate into a massive mess of metal and plastic when falling vertically with no Nr... no, it would not work.
Please refer to most helicopter manuals that state the importance of maintaining rotor speed. Good movie... totally fake helo ending.
Actually, it is feasible. However, the stars would have to align just right.
First things first, you don't need hydraulics to autorotate the rotor as it is a freewheeling unit. If it wasn't, the rotor would slow down in direct proportion with the engines and you wouldn't be able to autorotate in the first place. In other words, unless the rotor brake is on, the rotor will turn. We move the blades on the ramp all of the time without any power applied.
Now, depending on the aircraft, you will need hydraulics to run to flight controls. So eventually you will need to get your hydraulics on line to fly out.
Yes, you could start an engine in a free fall. The only problem might be that the blades would be flapping around alot.
Now to the real question could it be done? Again, possibly. The aircraft won't just start falling apart because it is falling. It will fall apart when it hits the ground. Plus, the helicopter was pushed out of an airplane so you will have some forward inertia changing your descent profile.
The next question is what type of rotor system you have. If you have a very high inertia system (think Huey or OH-58), the possibility of getting the blades turning fast enough to give you enough rotor speed is pretty slim depending on the altitude. The higher the better in these cases. However, if you have a low inertia system (think Eurocopters) you have a pretty good chance of getting the rotors up to a speed that you could effect an autorotation. I have gotten rotor systems to go from about 280 (or less) RPM to 380 RPM in about two seconds correcting for student mistakes during autorotations in the past so that is absolutely possible.
The next thing to consider is the fall. If you go out of the aircraft fairly level, the surface area of the rotor blades wiill keep the aircraft relatively level. Think of a piece of plywood going through wind, the flat surface always wants to be in the wind. it is hard to change its direction once a wind load is on it. The same will happen with the rotors. The wind will aerodynamically start the blades turning even if you are falling vertically. As the blades start to turn faster, you will become even more stable. The airframe itself will naturally point in the direction of the highest relative wind so you will have a relatively stable aircraft. Then as long as the rotor system continues to spool up, you will be good to go as, in most aircraft, your hydraulic pumps will come on line and you will then have control of the aircraft.
So now you are autorotating in a relatively controlled state and need to start the engine. No problems at that point as long as your engines work and you have the altitude to restart it. they start in the air just as easily as they start on the ground. Trust me on that one You don't have to be flat pitch to start them either. You also could have started the engines as soon as you went out the back of the airplane speeding this whole process along.
Now if you are rolled out of the back of the aircraft, you will have a lot more to deal with but the aircraft could stabilize and the process will be the same. In fact you could potentially start the engines while you are rolling and eventually regain control depending on the aircraft.
So, yes it is feasible. However, it is not advisable
