The cap smooths the output voltage from the regulator. The regulator limits the peak voltage by clamping the stator to nearly 0 volts after the output voltage exceeeds 14V or so. It resets at the beginning of each AC cycle. If there is no smoothing device (cap or battery) the lights just get a series of short (less than 1milliSecond) pulses of 14V. The higher the RPM, the shorter the pulses. It's likely there's nothing damaged at all besides your old dead cap. I'd get a new one, 6uF won't do much of anything. It probably won't hurt anything to try it, though.