No it won't move them. It will copy them! I'd strongly advice against this especially if you don't have enough disk space. As someone who tried and burned multiple times, this isn't how I sorted it out I felt you really want a clean migration like me only the Music folder no iTunes.
- Take backup of both iTunes and Music folder. Very important.
- Copy iTunes folder to external. Separate copy from backup. (Not necessary but hey another backup.)
- Now open Music app with option key pressed to create a new library and pick the .itl from external disk from step 2.
- This will result in something like you currently have except the iTunes folder will be on external this time.
- Once all is imported and working fine, I'd reset and consolidate like you suggested.
- After consolidation, try using library with external disconnected, and if everything works you can delete them from the external.
- Enjoy!
Important: don't try to symlink the iTunes folder and move it to external from the present setup. That bugged out on me multiple times. You have to recreate a new library and it will definitely work. I've tried it twice after having failed multiple times before with other methods. My library btw is ~300gb and ~29k songs.