If I understand your requirement correctly, you want to move files to a new drive and rename the drive itself.

Assuming the following,

You cleanly shut down all instances, move the files to new drive, and rename the drives to the original drivename.

When the instance start SQL will look for the file the location specified in system catalog, the files will be available.

Technically this should work. But you should have all backups and roll back options planned well ahead.