Using a stock WordPress installation, no.
WordPress, by default, stores uploads in the /wp-content/uploads/yyyy/mm/
directory for single sites. For network installations, it stores them elsewhere and maps a similar permalink structure to the new location.
I can see what you’re trying to accomplish by keeping things in separate directories, but you’d have to revise a large portion of the WordPress uploader to make it happen. Instead, why not ask a new question about how to protect original full-size images from the public but allow them to view a downsampled smaller version?
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