No, the CAT won’t change anything because it’s a linear transform and we do a linear minimization of least squares (let’s say… maths say all CAT are equivalent for our final step). What you need to tweak is the optimization strategy, for example optimize for skin tones or sky tones, or (worse case scenario) for neutral tones.
Notice CAT will change the delta E after white balance though, even if they don’t change the final delta E (after the whole calibration).
