Cross-Validation in Anomaly Detection with Labelled Data
After thinking thoroughly and having worked on the problem I mentioned, I will respond to my own question.
In supervised learning, we divide the data into three parts, namely train, dev and test sets. We use dev/validation test to see how our fitted model does in unseen data. What is unseen in this case, is the target variable, y_test. During training, y_train is seen by the model while y_test is kept unseen. In order to use every part of train and dev data, and eliminate the effect of chance, we do it K-Fold.
In case of unsupervised learning, the model does not see any y_train because only X_train is fitted. Since the model is not exposed to the labels, we can simply go with train and test set, rather than train, dev and test. In this scheme no K-Fold CV is required either because we can simply predict for all of the train + dev data at once.
Hence, it makes sense to use the labels of X_train, y_train, for validation during model development, and it is not required to use K-Fold CV.