no, assuming the emissions hardware is working correctly (and legitimately compliant to the standards.) starting in 2008, the EPA laid down the law and said diesels no longer get to play under looser standards. They were to meet the same emissions limits as gas engines in the same vehicle class. Which was a tough problem to solve due to the particulars of diesel engine operation.
background- for a long time now, gas engines have been able to clean pollutants from their exhaust via a relatively simple three-way catalyst. a 3-way cat gets its name because it has three elements inside it; one oxidation catalyst to oxidize (add oxygen to) unburned free hydrocarbons (turning them into CO2 and H20,) a second oxidation catalyst to oxidize carbon monoxide into CO2, and a reduction catalyst which reduces (strips oxygen from) oxides of nitrogen such as NO and NO2, turning them into N2 and O2. However, the oxidation and reduction catalysts require different environments to work efficiently. The oxidation catalysts work best when there is an excess of free oxygen in the exhaust, and the reduction catalyst works only when there is a deficit of free oxygen. here’s a graph of the efficiency curves for an automotive catalyst. See how brutally sharp the drop in efficiency is outside of that green band? So what gas engines do is continuously oscillate between slightly rich and slightly lean operation (within that green band) to keep all three catalyst elements doing their jobs.
diesels, however, always run an overall lean mixture (yes, I know that might seem odd given their propensity for emitting visible smoke, but that’s a separate issue.) An oxidation catalyst works fine to clean up hydrocarbons and carbon monoxide, but because of the constant lean operation, there is far too much free oxygen in the exhaust stream for a simple passive reduction catalyst to clean up nitrogen oxides. So diesel engines now need a completely separate reduction catalyst and a reductant fluid (e.g. AdBlue) to provide ammonia so the catalyst can convert the whole mess to N2 and H2O.
then they also need a diesel particulate filter (DPF) which is a very fine ceramic-matrix which traps particulates (soot) and holds them until the engine can run a regeneration cycle. which usually means a short period of adding additional fuel to raise the exhaust temperature enough to burn off the solid carbon. Although engines under heavy load also can kick off a “passive regeneration” where the operating exhaust temp is high enough to burn off the trapped soot.
for one, there’s a difference between federal emissions certification testing, and state emissions inspection. The certification testing is done by the manufacturer before the vehicle is allowed to be offered for sale, and is when the manufacturer certifies the vehicle will meet the applicable emissions standards over its useful life. State inspections (those that do them) simply verify the emissions control hardware is in place and functioning. IIRC many just plug into the diagnostic port, ensure that the readiness monitors report OK, and check for codes. if there are no codes, then it passes.
the states which do have testing tend to have different procedures based on the age of the vehicle. so a 2006 diesel w/o SCR and DEF isn’t beholden to the same standard as a 2018 diesel with that hardware.