Depends what type of differential.
Detroit Locker (if you want to consider that a LSD.. or a differential in general and not an abomination) biases 100% of torque to slower moving wheel, which for equal size tires is the inside wheel until it is slipped up to speed with the outside rear.
Anything with some sort of progressive locking, like a viscous diff or Salisbury-type (ramp & clutch) differential SHOULD effectively be biasing torque to the outside.. even if it's only "reactive" or passive. If it didn't, would be no better than an open diff, no?