If you have a limited slip diff, the additive helps the clutches disengage to prevent "chattering" around corners. The chattering is a stuttering feel like the two rear tires are fighting each other. You may also get a moaning sound on slow tight turns. Some say this is only noise and not harmful. I'll leave that discussion open.
The additive alone should not affect bearings at all. The additive is not a lubricant. If there is noise driving in a straight line, it may be the differential, but not the limited slip function of it. Pinion bearing, carrier bearings, wheel bearings can all go bad, irrelevant of LS additive, but not adding the additive is probably not related, IF it is a bearing.
A good shop should help you isolate where and what is making the noise and go from there. If the only change you know of is the diff fluid change, go back and analyze what fluid was used and the the procedure of changing it.
Best of luck!