My Aveo hatch back 2011 1.6 consume more fuel. Send it to my mechanic to check on it he said I should check if the converter catalyst is working properly, I sent it to exhaust specialist to check and he conclude that the converter catalyst is spoilt so I have to replace it. Please could it be the reason why it consume more fuel? I need help

When I'm driving in 3rd or 4th gear and the speed is accelerating, the car bucks and jerks. And it does the same if in low gear and the rpms go under 2000. Mainly in 2nd gear. I know I have bad oxygen sensor and catalytic converter.