You would remove zero or very low variance genes from the initial set to reduce input size and "noise": later, the feature selection strategy employed will assign lower or zero weights to genes not meaningful for the classification. Machine learning models learn what they see from the training set: it's very unlikely that a model could grasp something from the validation/test set if it has never seen it from training.

Read something more here https://scikit-learn.org/stable/modules/feature_selection.html