Quick conclusion: Not so good.
Details:
Here's a plot showing OPO length noise out-of-loop, in-loop, and OPO length noise without FSS engaged (pump laser not locked to PSL, out-of-loop). The OPO length noise with FSS engaged has a broad hump around 2kHz that was higher than the free-running laser noise. This hump was clearly visible in FSS fast path error signal. Once the FSS disengaged (but OPO was still locked) we get 1/f laser frequency noise with 232Hz harmonics on top of it. This harmonics disappeared when FSS engaged (at least that's what I saw today. Sometimes I do see harmonics at different frequency during OPO length noise measurement with FSS engaged). An investigation is on-going.
The high frequency part of length noise is likely to be limited by shot noise+dark noise combined but I would have to retake the dark noise measurement again to be sure. Hence those traces are not plotted here.
The OPO length noise was measured out of the I-MON of the demod box.
The loop UGF is at ~800Hz. During this particular measurement I forgot to turn the notch filter (6kHz) on. So, the UGF could be pushed a bit further but not by much.

