Yes a bad oxygen sensor can cause rough engine idle.
The oxygen sensor senses the amount of oxygen that is going through the exhaust and tells the computer to send either more fuel or less fuel to the engine so that it will run properly.
The bad oxygen sensor can also cause the engine to run rich because it can cause the engine to get too much fuel when it's not needed.
So if your engine is running rough and you smell the exhaust and it's running rich then an oxygen sensor is likely the cause.
I had an old truck that was running rich and running rough at idle and I put OBD tool on it and it told me that the oxygen sensor was bad.
I replaced the oxygen sensor and the engine started running properly and stopped running rich.
Some other things that could cause rough engine idle are bad spark plugs, bad spark plug wires, bad ignition coils, timing being off, bad timing belt, bad timing chain etc.
Your fuel injectors could also be partially clogged or not working properly which can cause a misfire and rough engine idle.