Yes, what you want to do has been done by many, but not me so details would be third hand.
If useful, I suggest you review tinyG schematics here:
and the go to this Forum at level:
and use the search capability , searching on Serial or…
Remember, tinyG is 3.3V logic, so direct wiring to UNO may not be appropriate (5V logic), but DUE probably OK (3.3V logic).
As you will see in the schematics, the Tx Rx you see result in a “wired OR” with the ftdi output and those terminals.
You can (carefully) use both channels simultaneously in parallel (a debugging hint)