No not normally. with the rear up do the wheels turn the same direction? You can also look at the tag on the rear and on the ID sticker on the drivers side code.
If you take a turn under power with a locker that is ture. But if you coast around a corner it unlocks and acks like an open rear. Hit the power and its locked up again.That is the difference between a LSD and a 'locker'. Remember, to turn a corner each rear wheel (all four wheels for that matter) turn at different speeds. You can go around a corner with LSD without any tire chirping because it is 'limited slip'. With a locking differential you would hear a whole lot of tire squealing every time you made a turn.