No, it doesn't look like it does. You have to re-import it from Box. Also, when you do that, it doesn't give you the option to replace the file, so it automatically creates a new file.
Example:
- Imported softwareiconTEST.jpg from box
- Updated softwareiconTEST.jpg in box
- Re-imported softwareiconTEST.jpg from box
- softwareiconTEST00.jpg is created and softwareiconTEST.jpg still lives on
Time to submit an idea!