Let's assume that a large military plane has its control surfaces disabled in combat. The engine(s) can still be controlled. There is a substantial number of ground forces being transported.
In theory could the plane be flown purely by distribution and redistribution of the weight of the passengers? Note these are military personnel and are used to acting on orders.
There are different degrees of control. The plane could at least be made to crash in a different debris pattern than if the input was not made, and even that's a form of control.
As the whether the plane could be controlled enough to land, and do so, as the question states, with all of its control surfaces disabled, let's see. You get considerably pitch control authority, with poor speed and accuracy, but very little direct roll control. Differential thrust provides a decent amount of yaw control.
So the first question is: Is the plane already on the glideslope of a straight-in approach to an airstrip? If yes, then passenger movement should, with some luck, suffice to get the plane down to the ground.
If not, getting a plane to a suitable landing spot becomes more difficult. Many military transports are designed for rough field landing, so over flat and easy terrain, it should be possible to get some sort of landing that is better than an uncontrolled crash. If the terrain is not so forgiving, it comes down to trying to navigate and fly with greatly reduced control responsiveness and precision, where many inputs will be made wrong, and down to whether they can be corrected in time.
To make an analogy, if a driver transporting a blind passenger falls out of the car, can it be controlled from the back seat by moving controls with the passenger's walking stick, acting on advice shouted from cars passing by? That's how trying to fly a plane that way would probably feel.
That said, much stranger things have happened. People have fallen out of airplanes without parachutes and survived. Planes have landed themselves smoothly after the pilot has ejected. And landings with a loss of most controls have happened as well.
Let us consider the longitudinal stability
In a longitudinally stable aircraft, any wanted or unwanted increase in angle of attack will cause the pitching moment on the aircraft to change so that the angle of attack decreases. Similarly, a wanted or unwanted decrease in angle of attack will cause the pitching moment to change so that the angle of attack increases.
The above stability is possible provided the aircraft has a stable centre of gravity
Modifying the CG by moving the passengers to modify the angle of attack is by definition playing on the instability boundary of the pitching moments, this is possible only with extremely reactive commands, that is with FBW (fly by wire) and not with FBP (fly by passengers).
Shifting the center of gravity by sending people fore or aft was once common practice on large airships to change pitch, taking advantage of a lever arm of several hundred feet.
It is theoretically possible to do this on a passenger airliner. Altering the CG with a fixed (frozen) elevator trim will have the effect of speeding up or slowing down the aircraft trim speed. Moving weight forward means elevator trim (aerodynamic) needs more airspeed to raise the nose (increase the angle of attack of wing), causing the plane to climb and lose speed, eventually settling into its new trim speed.
Moving weight back makes it easier to raise the nose, so the speed stability mechanism (elevator trim) raises the nose at a lower airspeed.
The key here is realizing the limitations of this technique. If the weight is too far back, the plane will not pitch down and gain airspeed before stalling.
A practical application of moving passengers would be to help flare the aircraft just before landing. Naturally, a little practice at altitude would help.
For a stricken aircraft, control by differential thrust has been demonstrated. Moving weight fore and aft could be tested.
