Yes, assuming the storage devices aren't locked from editing then in recent versions of Asset Bank there is the ability to migrate any Asset related files (original file, thumbnail, preview image, preview clips, large image popups etc.) from one storage device to another. Clicking on 'migrate' next to a particular storage device on the Admin > System > Storage Devices page will take you to a new page that shows you which other storage devices are suitable to receive the asset files.
Once you have selected a destination device to migrate to, starting the migration will take you to a page that refreshes showing the progress of the migration and the files that have been copied.
Things to note:
Migrations will only move Asset files. System files will NOT be moved.
If the migration is interrupted (by a Tomcat/webapp restart) successfully migrated assets WON'T be rolled back. Also there may be a single asset in an inconsistent state (i.e. files not where the database specifies, index not up to date) that needs to be fixed manually.