So before the update:No no, it doesn't work that way. If the Touch ID is replaced, the phone will continue working and the button continues to function like a Home button. The user can still use the phone and unlock using the pin code. Fingerprint scan is disabled tho.
Only after a firmware update does the system prompt an error 53. Which doesn't make sense if the phone is still usable prior to updating after the repair.
Replace button still works
After update:
Button doesn't work
Looks like they added something in the update to break it. Which means they did it on purpose. To stop tampering.