No because all the 10k uf capacitor does is keep the voltage stable / smooth the output of the rectifier. It keeps the lights from flickering at low RPM.
The DC-DC step up regulator I got is what keeps the voltage up at idle.
Here is a test I just did.
The camera recording this video has no battery and is only running off the power being generated by the moped.
The moped is running just a little above idle during most of this video.