I had a Jeep with limited slip diffs. On a road trip, I had the dealer change the oil due to contamination with the recommended synthetic lube They forgot to add the modifier. A couple of hundred miles into the trip home it started chattering and grabbing terribly on any kind of turn. I stopped and got some modifier at an auto parts store, put it in and a few miles later all was well again.

Based on that I would say yes, add the modifier.