There are shims on each side of the carrier between the case and the carrier that keep it in position, I think. I haven't done it myself, just have read some about it and also talked to the shop guys here at
Randy's. In actuality, it's a better idea to leave it alone unless it needs work. But if you really want to take it apart, you can.
Just realized that if you are dipping the case then you are going to have to remove the pinion and yoke as well, which requires a new crush sleeve, and resetting the lash, which I don't know how to do. Possibly replacing the pinion support bearings.
You'd be better off just masking and painting the case than going through all that trouble.