I am a couple of kinds of engineer and the most applicable here is marine (licensed ship's officer). The regular running of generators is probably left over from the coil lacquers used prior to WWII. Modern windings are not so affected. So, running at load will have little effect on the electric end.
This leaves the engine side. The biggest problem there and by far is the old fuel in the carburetor. If it is diesel, it doesn't have one of these. Old fuel can gum up the carburetor in fine style. Most manufactures know this and so provide a means to drain the float bowl and thereby eliminate the issue. So, if you do not believe that you will fire a generator/genny/genset/APU for some time, drain the fuel from the carburetor and save yourself a lot of grief.
It is my belief that the "monthly exercise the machine" is really perpetuated by the people that sell the parts that are damaged and worn by the regular running.
Matt
