If the pre-cat O2 sensor fails, the ECM is no longer able to determine whether the mixture is rich or lean. A pre-cat O2 sensor cannot fail silently, the CEL (check-engine light) will switch on. I am wondering whether the ECM has any other way for continuing to even try to hit the stoichiometric point, or will the engine be just running on either a rich or a lean mixture?
If the mixture remains always lean, the engine will overheat, then it's a matter of where one is: in cold weather the cooling system may be able to catch up; in hot weather it may not be able to keep up, and the cat may be damaged. Or the mixture will become rich and the driver may notice reduced mileage.