It is possible to connect the two SATA drives in the HDD expansion box of the TX1320M2 directly to the D-3373 mainboard SATA ports 5 and 6, without placing a dedicated HBA/RAID controller.
In this case I used the Supermicro CBL-SAST-0631 HD MiniSAS reverse breakout SATA cable.
The two drives were instantly recognized in the BIOS and the server booted without any problems.
So technically it is NOT required to use a PCI-e HBA / RAID controller when adding the two drives in the HDD expansion box. You can also use this special cable and use the SATA controller on the mainboard.
Keep in mind that hardware raid for the two drives in the expansion box is not available and I have not checked the speed performance of this setup and I do not expect Fujitsu to support this configuration.
But it works perfectly for adding all six drives to my ZFS pool(s) in Proxmox 5.3. And as an extra benefit, the system remains a bit cooler and more energy efficient without the hot-running PCI-e HBA / RAID controller.