When operating correctly, the O2 sensor cannot cause any smoke. However, if the sensor is faulty, it can cause your car to run rich or lean. If your car runs extremely lean for a long period of time, you could cause severe engine damage, resulting in black or white smoke from the exhaust.
I don't think so, I has an older Pontiac sunfire with a bad o2 sensor and it never smoked. If the smoke is a bluish color and smells bad it means your engine is mixing oil and water..... Bad news. Hope you get some better answers.