Yes, it will do all of that.
However, I would recommend that you make a backup of the database and the image folder beforehand (as I would recomment before any such 'major operation'
) and personally, I would copy rather than move the images, and only delete the source files once I'm satisfied that the operation has been a success.
You will also have to assign a volume label to the new drive, but I guess TP will prompt you for that if the drive doesn't already have a label.
Afterwards, you may want to do 'Database | Advanced | Compact & Repair' to physically free up the space from the old thumbnail records in the database file (if you've used the two-step Copy + Delete appoach rather than Move.. I don't think that Move alone would generate new records. Actually I'm not sure, but it won't hurt, so I'd do a Compact & Repair anyway).