When the car is running closed loop each bank is handled and dialed in so to speak for AFR on its own. There is code in place that actually will fail out the O2's if the difference is too much between the two. If your only monitoring one side, the other bank could be running rich and nobody would know it and your wasting fuel, or go the other way and it could be running lean and kaboom!!!
Your much better off with both O2's working properly.
Frit