Guiones,
You are right, it updates regardless of GPS primary, but with GPS primary it is not necessary to insert the TO Shift as the system will take the GPIRS coordinates at the application of FLEX/TOGA. Whereas, if you are flying without GPS primary you are giving FMGS your exact location of take off (by inserting take off shift) at the time when you move thrust levers to FLEX/TOGA.
Our company policy is if GPS primary no need to insert TO Shift, otherwise you do.