Mmmmh….That will not make sense to me. If the engine does not run, the flow control valve inside the pump is in the "closed" position, which will effectively cut off the connection between the pump and the steering gear. I cannot see, how moving the piston in the gear will "suck" fluid out of the reservoir.
But if that method works for you, Dan, more power to you.
Sometimes "engineering science" does not have an explanation for everything.
Mike, the valve you make mention of is an over pressure valve, and will remain closed until hydraulic pressure from the locking of the steering wheel (full left lock or full right lock) opens it. It's in place to prevent excessive pressure build up when in full left/right mode. Otherwise oil would spew out of every O-ring and radial seal on the high pressure side of the pump and gear box. What you call a "flow control valve" is actually a "pressure" valve, and is located inside of the steering gear box itself. It is actuated by movement of the steering wheel. It essentially directs oil under pressure to the front or rear side of the power piston inside of the steering gear box.
Benz Dr.'s method of bleeding the system is, in fact, a very easy and fool proof way to bleed the system of air. By moving the wheels left to right WITHOUT the engine running causes the power piston to literally suck oil into the system, and when moved in the opposite direction the displaced air escapes through the reservoir. You must remember that the procedures listed in the BBB aren't always the best, correct, or easiest methods. The BBB isn't the law.....it's only a suggestion.
You mentioned that you don't understand how moving the piston in the gear will "suck" fluid out of the reservoir. It's simple......imagine a syringe sucking a liquid up into it. The only difference is in a syringe there is no air to displace, and if there is you simply turn it needle side up and depress the plunger until the air bubble has escaped through the needle. An even better example is one of those under water water pumps you use in something like a koi pond. When the system is new or has been serviced the water lines are full of air. As soon as the pump starts moving water the water displaces the air in the lines until the lines are full of nothing but water. Likewise, the more times the power piston in the steering gear box moves from top to bottom, and them from bottom to top, more and more air will be displaced. Though, during the process keep the bleeder screw open and plug it off with your finger when the power piston is on the down stroke. Otherwise it'll constantly suck air in. On the upstroke of the power piston release your finger off of the bleeder screw. When oil starts to emerge from the bleeder screw all/most air has been displaced. Any residual will be displaced by running/driving the car. Even if you didn't bleed the system at all the system would eventually displace all of the air on its own. It would just take several miles, initially no power assist, and putting up with some groaning from the system until all of the air was displaced.
There is ALWAYS a hydraulic connection between the pump and the steering gear box. There is no valve that prevents this (except when in full lock left/right). There are several ways to achieve bleeding the power steering system. The methods listed in the BBB and by Benz Dr. are the easiest, cleanest, and less time consuming methods. All methods lead to the same end result. How you get there is your choice. Just keep an open mind about how to approach things like this. Never take the BBB seriously, and never overthink the process or try to improve upon it.