In my opinion and as per logic, bad quality of fuel has to do something with the choking of Catalytic Converter, not the engine oil, as exhaust gases from the engine block / choke Catalytic Converter.
Engine oil never comes in contact with catalytic converter, unless / until seals, rings, pistons, etc. are worn out, engine oil gets burnt and via exhaust gases, it comes in contact with Catalytic Converter.
During normal conditions, and when engine is absolutely healthy, seals, rings and pistons are strong, engine oil max. reaches up to the rings, installed with pistons, and it never comes in combustion chamber.