Nope - if you read the bobistheoilguy report, the stabilizer breaks the balance of additives that come with the gear oil from the manufacturer and actually make the "stickieness" of the oil worse

Just put a good quality gear oil in there. If you are really worried about gear oil sticking everywhere, drain out and put redline in there (not sure about redline for LSD diffs tho). It was pleanty sticky by itself out of the bottle (read Bob's reoport for details).