Yes, it seems to me that logic dictates that it would have to compromise the LSD performance to some extent, however small, and you're better off living with "the noise," since it only occurs on low-speed, tight turns. Given other manufacturer's experiences in LSD cars with big tires, it seems clear that some just can't tolerate hearing what they perceive to be an objectionable noise.
The friction modifier additive was exactly what GM told dealers to do when customers complained about C6 Corvettes, but they were also quick to point out in the service bulletin, that no action was necessary, except upon customer request.
Greg, my Z06 did the same thing, and the noise didn't show up until about 2K miles. I never bothered to have anything done about it.