Elements does not move or copy your images (unless you specifically tell Elements to do so). So, the photos are on your hard disk wherever you put them.
IS there a way to have My Pictures folder be as neat as elements
Perhaps you need to think about this a little differently. If you have organized your photos in the PSE organizer, you no longer use your operating system to organize/find/search/browse your photos. From now on, when you want to find a particular photo(s), you use the organization that you spent time to create in PSE. That's the whole point of the PSE Organizer -- it gives you tools that are different, and in my opinion superior, to what you have in your operating system.
So I do not ever delete the folders because the PSE just provides the organization shell. IT wold seem that I would then just minimize the folders to avoid the distraction.
All of this is correct. I never look through my folders to find photos. I use PSE to find them, and if I need a specific photo outside of PSE, I use File->Export->As New File to a temporary location.