Most alternators have a lot of inductance in the windings. The open-circuit voltage of an alternator is often many times the running voltage. That is why load-dump on a car alternator is so severe and why voltage regulators on AC generators are so important.
In constant current, variable speed applications, the large inductance is used as a current limit. That applies in car alternators and in directly driven AC lighting like on bicycles and some small motorbikes. The current is largely independent of voltage load at higher speeds. I was able to change my motorbike lighting (1983 Honda CG125) from 30W at 6V to 60W at 12V with no change to the alternator, but it was dim at tickover.
On the wind generator, the capacitors in series will form a tuned circuit with the inductance of the windings. The impedance of a series tuned circuit is less than the scalar impedances of the inductor or the capacitor. The lower impedance may increase the current a lot. It isn't breaking any thermodynamic laws, it's just bypassing a current limit.
It is quite possible that the generator takes more shaft power and slows the turbine more, so takes more power from the wind. The shaft power is difficult to measure, and it isn't fixed for any particular wind speed. At zero speed, or at zero load, there will be zero power. Maximum power will be at somewhere around half the zero load speed, but it is unlikely that a small wind generator manages to hold the turbine close to maximum power speed all the time, and that is where some improvement can be had.
The downsides could be:-
The current limit is compromised, so there could be damage to the alternator if it is designed around the natural current limit.
The batteries could be charged too fast.
The effect will only be at its best at one wind speed, as there is only one frequency that gives best tuning. However, there could be some improvement at all useable wind speeds.
I agree that AC currents from wind generators are difficult to measure.