Here is an amplitude spectrum plot of y-arm cavity noise with a 50 Hz cutoff damping filter of the form zpk(0,[50;50],1). The low passing of this filter was intentionally extremely poor in order to see the damping noise in the cavity. The blue trace is the noise with no damping, which may be considered the 'best case' scenario from a noise point of view. The green has regular local damping on the ITMY. The ETMY has no damping for this measurement because the cavity control feedback to the ETMY takes care of its control when the cavity is locked. Notice the the large increase in noise from 40 Hz to 250 Hz, up to 1 order of magnitude. This noise is from the OSEM sensors passing through the damping loops. The red curve shows the y-arm noise with the exact same damping, except it is now applied in the global scheme. In this case, the damping noise falls completely below the baseline level of the cavity and becomes indistinguishable from the 'no damping' case.
If the damping injected enough noise I'd expect we would see a drop of 50 to 80 times switching from local to global. That is, the same factor measured in the transfer functions listed in log entry 8193. However, the damping noise is only at most 1 order of magnitude above the baseline in this measurement. We would have to increase the damping noise by about another order of magnitude before we could expect to see the global damping noise in the cavity measurement.
The units of the cavity displacement in the plot were calculated using the 1.4e12 counts per meter calibration in log 6834. The measured UGF of the LSC loop at the time was 205 Hz. The peak in the plot above 200 Hz appears to be from this unity crossing. Moving the UGF also moves this peak.
Moral of the story: global damping can isolate the damping noise pretty well from the cavity signal.