Yes, but right-click drag means clear visual confirmation of the action, the physical movements are the same for all types of operation, and you can make up your mind what to do after you've indicated where. I only use shift or control if I accidentally left-click drag.
The Right-Click Drag context menu is also an Explorer Shell Extension Point (going way back) and some apps can add additional behaviors to it beyond Cut/Copy. 7-Zip for instance includes a lot of options in a sub-menu. For instance, Right-Click Drag a set of .zip files in a Downloads folder to a more permanent home folder and you can select 7-Zip > Extract to *\ and 7-Zip will expand all of the .zip files into folders based on the names of the .zip files.
