The energy consumed by a machine depends upon the efficiency of the machine and the work done. Mechanically adding another set of blades to system doubles the work done plus using a mechanical system may decrease the efficiency of the total complex. It seems unlikely it would save energy plus the clumsiness of a mechanical system described would decrease the capability of the system to facilitate cooling over a larger area. Two separate fans provides much more flexibility for the system.

Even if the extra mechanical linkage wasn't any less eficient, it would cost much more than simply buying another fan. Most fans are direct drive, that is, the blades are connected directly to the armature shaft; introducing belts and pulleys or chains and sprockets would decrease the already efficient transmission of power. I just bought a 20" "breeze box" fan, new, for under $10.

Actually it is possible to make your idea work efficiently. I think if you were to use to seperate fans with lets say with 20 to 30 gear spokes and the motor with 40 to 60 gear spokes you could efficiently produce twice the cooling that you are requiring. I think what you have to way is the ratio of how many spokes that you want per gear. My theory is that the smaller gears will turn twice or maybe three times the revoloutions that the big gear will and maybe the motor will not exort to much energy depending on how you have it configured.I think its a good idea. It is very possible.

If you want to get more air flow from your fan, it will be far more efficient to simply put one larger diameter fan on it instead of two small fans. Any gears will reduce efficiency. Gearing the fans to turn faster will increase the load on the motor.

Believe it or not Air is very hard to move. Putting two blades attached to a motor that was rated for one blade would cause over heating, slower rotations, possible fire in time from the motor burning up. I can give you an example--try pulling or carrying almost all the weight that you can, then double it--same way with motors, small motors-small blade, larger motor-larger blade or you can look on the name plate of different fans and see the differences in hp to blade sizes (also shape of blade)