If you swap the whole diff then yes. The better question is why, when you could find a cheap lsd. If you are already going through the effort or paying labour, may as well do it properly.
I cant find one in alice springs and postage is gna cost me more than the diff if i get one off ebay. If i remove the diff and take in to a mechanic is it gna cost me around the same price to get the lsd rebuilt?