You might get the rust off but the rust has compromised the surface of the gear. The damage has been done. It has pitted the surface which will screw up your oil film ad create high stresses in the gear face, possibly causing pitting with some use..
It might be fine for a stock 3.8 but knowing you it's going behind something rowdy and won't last.
What's the gear ratio? If it is decent I vote for the electrolysis method. Unbolt it and hang the whole carrier in a bucket of washing soda. But I beleive the pinion pin bolt is going to be the deal breaker.
I'm guessing that is a 7.5" rear???
Like has been said, the gears are toast.
I would definitely try and save the carrier though. I have used both methods for rust removal that have been mentioned having better success with the electrolysis method.
Anyone ever used Evapo-Rust?
I'ts great stuff but after you rinse the part off per instructions put something on it to protect the surface from rerusting. I'ved used it on alot of rust metal. But the really bad stuff it may not cut it all, that would be for a blaster then.