Interestingly, GM (and thus the TMs) call for an additive to be added. However, Eaton, who makes the Detroit Locker units, says no additive is necessary. Personally I'll trust the company that made the component over the generic GM warning that gets slapped into plenty of manuals whether it's needed or not- but then again, for those who choose to run the (well, any) additive, it won't *hurt* anything, except maybe your wallet. The front posi unit, however, I believe actually *does* need an additive.
I run synthetic trans and gear oils in all my vehicles. The main advantage is that it lubricates better when cold- so when I fire the truck up in the snow everything will be lubed rather than having a gear oil jelly sitting in there. The Miata is the only vehicle that gets synthetic motor oil, though (only Royal Purple, Redline or Amsoil)- none of the other vehicles deserve that.