I've studied many questions and answers on the theme of nested cross-validation. I understand why we need it and how I can, after that part, find the optimal hyperparameters and any other things I'm interested in.
But here I'm interested in the following scenario: I want to build a classification model using, say, a RandomForest. So, for my model I want to pick the hyper-parameters, choose between two different preprocessing schemes and a get an unbiased estimated of the generalization error. Let's also say that I consider preprocessing to be part of the 'model building process'.
My question is do I need a nested nested CV (inner loop: hyperparameters, outer loop: preprocessing, outmost loop: generalization error) or can I stick with a nested CV and treat the different preprocessing schemes as just another hyperparameter? In other words, can the inner loop treat both hyperparameter and preprocessing selection?
An answer is given by @cbeleites here, but it is about selecting an algorithm and not a preprocessing scheme. Does this hold for preprocessing as well?