It depends whether the [-12v, +12] will allow to reach the stability limit at which the ultimate gain Ku and the corresponding period Tu are obtained.
I think you can remove the saturation for the tunning purposes and that the calculated PID parameters will remain valid after putting the saturation back.
Yes I agree with amine that for tuning of PID controller you have to remove saturation and then go for closed loop zn tuning. You can also go for open loop tuning of zn in which you have to remove saturation you can use this for reference
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