I think it's only checked for leaks if it even has a cat installed. I had mine inspected a few months ago and looked it up on the TX DPS website and there is no emissions testing for vehicles 25 years or older BUT the exhaust must not have any leaks or rust holes. As for my inspection the guy just walked around it and said "Nice YJ", typed something on his computer and handed me the bill. Who am I to argue?
Another option is to get Antique tags for it and there's no inspection but it has restriction which may limit your daily driving.
I also got an exhaust quote from them earlier and he asked with or without a cat. So that may answer your question.
That's what I thought, I knew about the 25 year rule but wasn't sure if they inspected for factory installed equipment.
I believe I'm going to put new exhaust on it with no cat.
It shouldn't be an issue with the inspection as long as there are no leaks, but I don't see any reason to remove the cat, in general. I hate the smell without one and there is no power to be had or any other crap to be improved by removing it.