This should be possible
The HDD's must be connect to the Motherboard in the Way that the 128 GB HDD is Drive C and the 1TB HDD is Drive D.Disconnect your 1TB HD from your Motherboard (only to be sure that Recalbox is installed on the right HDD) Install Recalbox on your 128 GB HDD Shut down your PC, connect your 1 TB HDD (be sure it is formatted with the exFAT Filesystem) and then start Recalbox again. In the Main Menu go to SYSTEM SETTINGS -> STORAGE DEVICE
Your 1 TB HDD should be listed here.
Select it and let Recalbox reboot.
You can read the Rest here
under "Configure Recalbox to use a USB storage device"
You don't have to worry because it's describe how you use an USB Stick or an external HDD, it should work with an internal HDD too.
And you don't have to synchronize your HDD.