This is the ceiling-fan motor with its original stator and rotor.
Only thing I did was to make a hollow ( pitch control) shaft with heavier ball bearings in it to attach the blades.
Now if you drive it above its nominal number of revolutions per minute:
Will there be a chance then that it starts functioning as a generator?
It has a two-phase winding.
The ring looks like a "squirrel cage" - a conductive component dragged around by the magnetic field from the coil/laminate assembly and the magnetiztion from the eddy currents that field generates within it.
If you connect a capacator across ONE of the phases to make a resonant circuit (leaving it otherwise unconnected), leave the other unloaded at low voltages (for instance, by hooking it to a rectifier and battery, which won't pull appreciable current until the voltage gets to the battery voltage plus two diode drops), and the rotor has a bit of residual magnetiztion to get things started, when you spin it up to where it's going a tad faster than the RPM corresponding to the resonance, you should start pumping energy into the "ringing" of the tuned circuit - up to the point where the core is saturating. It will start "fighting back" to try to keep itself from spinning appreciably above that RPM.
At that point the magnetic lines that are "nearly pinned" by the eddy currents in the rotor will also be dragging through the other phase's winding, generating a voltage and transforming shaft HP into electrical energy you can harvest.
There are substantial downsides to this approach - among them that (like a wound field) you have copper losses, both in the resonant winding and the rotor, and that it only works at a narrow range of RPM. Nevertheless, it can give you nontrivial generation without further conversion of the rotating electrical machine to add either magnets or a field coil to the rotor.