Yes. The Godox TT600 can be triggered by cable through its 3.5mm sync socket, so an Arduino-operated relay setup should work in principle.

The main issue is timing. If your Arduino triggers both the camera and the flash directly, the flash must fire only when the shutter is fully open. If it fires too early, the frame may be dark or only partially exposed. When a flash is triggered by the camera, that timing is handled automatically, but with an Arduino you need to manage it yourself.

So the basic answer is: yes, it should be possible, but you may need to add an appropriate delay between triggering the camera and triggering the flash.