I called the ARB phone number and asked the lady there. She answered if it was before the cat it requires a CARB# no matter what part it was. She didn't sound to confident answering me, thought I get a second opinion.
Are you sure it was an "aftermarket" oil cooler?? Some vehicles have "factory" oil coolers,
NO CARB EO# required.
I have to say you are over thinking the oil cooler thing,
it has nothing to do with emissions. I cannot "see" where an oil cooler would
"vent" emissions into the atmosphere.
It was connected to the power steering pump out to the device, Tee'd to the cooler.
When I called ARB, the lady that answer sounded like she didn't have a clue. I told her it did not have anything to do with emissions. She replied, if it is located before the catalytic converter, it requires a CARB#.
I also looked at the CARB website, look down menu. There is nothing for oil cooler, only oil filter relocating kits.