Is It Ok To Do 0-1 Scaling Then Divide By The Standard Deviation?

Rookie here tryna learn and I read over normalization so I had a question google couldn't answer

If am understanding stuff correctly, if I have a df I can first do 0-1 scaling on it to get equal ranges while preserving the data series's original means and standard deviations and then once I divide the 0-1 scaled data by the standard deviation, I would get a variance that is 1 across all data series.

Therefore my brain concludes that doing …

datascience deviation scaling standard