I have welded a diff or a race car before. The differential needs a lot of cleaning for the weld to be proper and penetrate. I would NOT do it for a street car. Everyday driving and getting out of parking spaces will be a nightmare. Your engine mounts and transfer case might not survive long either. There are reasons why manufactures offer limited slip and not no slip.
Wouldn't do it. All the "drifters" here weld their diffs. Surprisingly big scene here. Everything from 240s to S10s, all rat bagged and sticker bombed.
Issues as mentioned. Also uneven tire wear if its your daily. Turning will be fun... chirp chirp chirp as you go. It's illegal to do, here at least.
Why do YOU want to weld it?