Does it make sense to use this StandardScaler() with no parameters for features following distributions other than normal distribution ?
What do we do in this case ?
That is somewhat a broad question. Maybe you can take a look at the documentation here to get an intuition on how different scalers behave when dealing with outliers, or here if you prefer a more technical description of the scalers offered by sklearn.
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To complement Arturo’s answer above, keep in mind that the choice of the numerical preprocessor has an impact on the inductive bias of the full pipeline and its hard to know ahead of time what will be the precise impact on the cross-validation score.
A pragmatic answer would be: try different kinds of preprocessing strategies and see what works best and most robustly using cross-validation.
It’s very often the case that you can replace a StandardScaler by a MinMaxScaler and get very similar results. From time to time, very different preprocessors such as QuantileTransformer can yield to significantly better (or worse) results than StandardScaler or RobustScaler but it’s hard to guess ahead of time.