No, but NOX formation is far more complex than SOX formation, due to nitrogen in the air being present along with nitrogen in the feedstock. Hotter combustion temperatures which are desireable for thermodynamic efficiency create more thermal NOX from nitrogen in the air. So thermal NOX formation is greatly influenced by combustion apparatus design. Only way to completely avoid around thermal NOX generation from combustion is to use pure O2 for combustion which is not feasible from safety, logistics, or air seperation (or water cracking) energy efficiency to generate the pure O2. Having said that, refining processes which reduce sulfur in fuel also reduce nitrogen in fuel.
For CO2 emissions, I don't believe that would significantly change, but have never studied it per se on less refined vs. more highly refined petroleum derived fuels nor know of any such studies. Most combustion control, coupled with environmenal conttol, of industtial combustion processes target a certain max threshold of CO for fuel efficiency, safety, and pollution control, thus maximizing the CO2 produced from the fuel. This is up to including precious metal combustion promoters containing platinum and / or palladium to drive combustion completion in some cases.