It could. When my O2 sensors were bad, it was running real rough, bad gas mileage. Rockauto has the cheapest O2 sensors. Got my bosch's for $23 each, vs Autozone & PepBoys for $56 each
Yes, when o2 sensors go they can cause big issues. If you suspect there is something wrong with the o2 sensors than I would suggest changing them. It will only make your car run better whether it's your main issue or not. I had one completely die on me after installing exhaust and headers on my car. Made the car stall all the time and run super rough. Changed it out and it fixed the issue completely.
Actually may have been bad for a little while it's never run better I'm thinking someone disabled the CEL light because mine does not come on but wheni hook up the scanner I found it