That's the ring gear engaging, since there is no fluid its much more audible. Now if that's normal or not I couldn't tell you since I've never had a z31 lsd. Doesn't look like it has a lot of play in it though, and as Plata said, when there's fluid in it, it could be perfectly fine.
If it's been sitting without oil in it though, I would at least take the rear cover off and check for rust on the bearing surface areas