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You have to rob Peter to pay Paul. If you are removing thickness, you are reducing bearing preload.
Yes, it should. Are you measuring side clearance?
There are plenty of posts on the forum in regards to this subject. Keywords, pinion depth, backlash, gear tooth contact pattern should all yield some good results.
Side to side = carrier bearing preload. So if it's good then you will have good long term results.
You measure it by affixing a dial indicator to the side of the ring gear. Pry the carrier from left to right and right to left. The recorded measurement on the dial indicator is your side clearance. You will have to force it in and out unless you have a housing spreader.