I do not think it will quiet the loudness of the Quaife LSD very much because the gear noises you hear are from them being pressed against the case. (How the Quaife works by design and why it requires a forged casing)

Yes "theoretically" the fully synthetic MTL should help some due to it's better sheer stability & lubrication properties.

2000 SVT #674 13.47 @ 102 - All Motor! It was not broke; Yet I fixed it anyway.