The sensor only makes the warning light come on on the dash, it doesn't send any signal to the ECU.
I changed my fried cat and couldn't get the sensor out so I just cut it and blocked the hole in the new cat with a bolt.
The light comes on and goes out when the car is started.
Your cat may be blocked, or your not starting problem could be totally unrelated...
Try removing the cat and starting the car, if it starts, smash the guts out of your cat, reinstall and buy a new cat ASAP.