That's the natural desire, but it is often not straightforward.
It depends on the feature of your LF boost, but in general a LF boost yields a huge gain at DC. Every circuits has some small mount of DC offset and it is amplified by the boost.
e.g. Suppose 1mV input-equivalent offset with DC gain of 10^4. This causes the output of 10V.
What you may be able to do is put an offset to the FFT analyzer output such that the output offset of the box is nulled. If you are lucky, this would let you measure the boost TF.
Even if you have some offset in the servo filter, usually it is not the matter as the servo try to squeeze the offset by the feedback.
Usually small input-equivalent offset of the servo filter turned into huge offset at the output of the filter module, if the loop is not closed.
Once the loop is closed, the feedback signal is adjusted such that the error signal cancels this offset.
Of course, the actual situation depends on how much offset you do actually have. So the above mentions are just general comments.
Trying to take a TF with the BOOST on (to emulate the state of the system while running the gyro) proved fruitless, as this causes the output to rail regardless of how low you make the source or whether you go in at SWEEP or INPUT. This is problematic because we would like to do the closed-loop measurements on the actual (BOOST on) running state of the gyro. It is possible that engaging the boost produces an unwanted offset, and this would explain why doing so with the cavity locked sometimes causes it to drop. I will take a look at the schematic to see if something is obviously wrong with the circuit.