Yes but since incomplete combustion is inverse correlated with fuel efficiency (unburned fuel is wasted fuel), it's not really a trade off. What is a trade off is NO emissions vs fuel efficiency. Burning your fuel oxygen rich will burn of more fuel, but also makes more NO (due to higher temperatures if I remember correctly).

Those eventually degrade to CO2 so the increased warming from them compared to co2 by mass is temporary, like with methane.