Of course, the runaway in question should not be understood for a given machine, but in relation to the principle (sic!) Invoked and which demonstrates the absurdity: an energy that would increase itself to infinity ...
You write:
But if someone has the data in question, the calculation can then be done according to the most basic rules known.
The system described can be likened to a lever-arm effect: the energy consumed by the compressor is, according to the promoters, low, but would be converted into a higher power thanks to the Archimedes thrust. Why not? The torque transmitted to the axis can increase if its speed is reduced in the same proportion ...
Where the shoe pinch is that this speed must then be multiplied to drive the alternator => decrease in torque and we are left with the initial configuration, less losses ...
With a lever I can lift a load too heavy for my strength, but, in return, I would produce a large movement in exchange for a minimal movement and slow. If it were necessary to move very heavy loads quickly, there would be no alternative but to increase the initial power.
These are the most basic rules known ...