Yes, there are occasions when they will help out with traction, and that's what they are designed to do. Then again, the traction control system will do a similar job, and that's probably why the LSD, which was standard on the Senator, got dropped on the Omega.
TC with an open diff has the advantage that it makes it less likely for inexperienced drivers to spin the car when they find the limits of adhesion, because an open diff provides a "safety net" of disabling torque to the outer wheel when the inner one loses traction. Then TC disables the engine, then re-enables it, then disables it....etc
Adverse weather aside, I think the only scenario when an LSD is nice to have, is nipping out of T junctions quickly or exiting roundabouts where the inside wheel letting go can stunt your progress if "pressing-on".