No, my noise is always there. It's got to be a pivot bushing or mounting bracket flex or something like that in my case. It's not as loud as yours though.
Yours definitely sounds like it is coming from the pedal assembly. It sounds like the pitch is changing as the pedal travel changes. Or, perhaps your for clutch fork or spring plate are making the noise. It is just hard to think that something full of fluid would make a friction noise like that. But, IDK, just my guess. Have you lubed the entire pivot and pedal bracket assembly with WD40 or something similar? Remove the slave cylinder and grease the cup that the slave piston sits in? No way to lube the clutch fork without separating the tranny I think?