I do not know how files are saved on a Mac, but the Elements Organizer does not maintain a duplicate copy of your photos. It is only a database that points you to the files on your computer. Your files remain wherever you want to keep them on your computer. When you save an edited file in the Editor, you are given a choice as to where and how you want to name it. The default is to give the file a new name with a suffix attached to the original file name, such as "-edited 1". You will also be given the choice to save it in the Organizer, in which case the file will automatically show up there. You can also maintain it as a "version set" in which case the original and edited files will be stacked in the Organizer so only one thumbnail appears in the grid.
If you don't want to keep the original file, you can delete it in the Organizer and you will then be given the option to also delete it from your hard drive. Alternatively, when you save the edited file, you can give it the same name as the original, in which case the original file will be over-written on your hard drive and you will only have the edited file.
No matter what, the files will remain on your computer hard drive until deleted or over-written and can be found by any search engine you use such as Finder.
It is best to delete files in the Organizer. Otherwise, the thumbnail will remain and will appear as a "missing file".