This is possible, however you will need to create a batch file (could be placed inside this folder you mention) that people would drag-and-drop file onto, which will do the following:
- Gets the drag-and-dropped file as an argument/parameter that the batch file can use.
- Checks for files with the same name as the dropped file
- If the dropped file's name is unique, then save the file
- If the dropped file is not unique, then first rename the conflicting file to filename_backup.ext, then save the file
Doing the above, you will achieve what you are looking for. Of course this means you will have to educate/force all users of that folder to always drag-and-drop files onto this special batch file.
You could place this batch file at the root of a folder and then save the actual files to another sub-folder so users will immediately notice that they have to drop the file onto the batch file.