If I am understanding you right, you want to copy the OS from a new MyBookLive without opening it? And then copy the OS to a new hard drive that you are gonna put in the old MyBookLive enclosure?
If so then yes, login to the working mybooklive via PuTTY and issue the following command to copy the os partitions to your public folder.
NOTE: The 2 MyBookLives will have to be the same size or you may have to resize the data partition.
If you are cloning a 2TB to a 3TB I believe the 3TB drive will only show up as 2TB because you have cloned the partition table
dd if=/dev/sda of=/DataVolume/shares/Public/mybook.img bs=1M count=4700
Copy mybook.img to an 8+gig NTFS usb device
Connect the new hard drive to a sata port on your computer
Boot Linux Rescue CD
Use gparted to figure out where your drives show
In terminal type:
mkdir /mnt/mybook (creates mount dir)
mount -t ntfs /dev/sda1 /mnt/mybook (mounts the usb drive with mybook.img)(May show up as sda1, sdb1, sdc1, etc in gparted)
dd if=/mnt/mybook/mybook.img of=/dev/sdb bs=1M (Copies the os partitions to the new drive)(May show up in gparted as sda,sdb,sdc, etc)
Put the new drive in the enclosure
Boot it up
Quick factory restore from the Dashboard to format the data partition