Possibly, he said the first time he took it in they failed him for not having cats but then each time after that they didn't care. It has a mild 350 crate engine (from what it looks like) with long tube headers and true duals, none of which looks factory.
Talking about adding cats to clean up the exhaust on a big-cammed or out-of-tune car... Catalytic converters need to operate within a specific temperature range and also need to have the AFR as close to stoich (14.7:1) as possible or they don't last very long. Too cold and/or too much unburned fuel and the substrate material just gets coated with junk and stops doing its thing after a while. Modern cars vary the AFR between slightly rich and slightly lean as you drive down the road to keep the cat(s) working at peak efficiency and "clean" inside. Air pumps were used up until the late 2000s on some cars depending on how much extra O2 the cats needed based on how the engine would burn the fuel.
Up until it got wrecked I had to get my '93 Jeep Cherokee e-tested every 2 years; running a cheap aftermarket cat I'd typically have to replace it every 3-4 years. I later found out that because the 4.0L was never equipped with EGR, the cat(s) wouldn't last as long as in other engines with EGR because there was a lot more NOx they had to "filter" out. EGR (especially if it's cooled) does wonders to reduce CO and NOx and can also boost fuel economy quite a bit, and like vacuum advance has no effect on performance because it only works under light loads.