The F & P was designed as a motor, it is about as unsuitable a construction for an alternator as you could imagine, but it is cheap and easily available.
Running alternators into leading power factor loads causes rising rather than drooping characteristics. With a type of winding that inherently has a high inductive reactance the benefit of capacitors will be considerable in that in will let your output increase with speed whereas it would normally tail off at constant current.
For hydro this would be a great advantage. For wind it may or may not depending how the components of reactance balance the stall issues with the prop. I suspect it would be an advantage as long as you use modest capacitor values to just increase the slope of the power curve in the high wind region.
For the Hugh Piggott type machines just forget capacitors, they never become reactance limited and there is no benefit from maintaining a leading power factor that increases the rms stator current, adding extra copper loss. Unfortunately the capacitors can't even correct the rectifier power factor as it is a waveform rather than phase phenomena.
In some cases there may be an advantage for motor conversions but in general the frequency is too low for it to be practical for low voltage machines.
Flux