We have absolutely no inspections up in MN, ND, I drove around an Escort with one working brake (3 including the required E-Brake), I also drove a Beater buick with a total of 5 exterior working bulbs, 2 headlamps, 1 tail, 2 front blinkers.
But, of all the cars I've owned (16 or 17) the only one I removed the cat from was my '86 Lincoln, which couldn't go more than 80mph due to exhaust being so plugged, turned out the cat broke, and the chunks were perpendicular to the flow. Even my '83 carb'd tercel had a working (original?) catalytic converter and +240,000 miles, I was trouble shooting the rough idle one time, and the cat was working so hard it was GLOWING orange in daylight! '86 tercel had well over 300,000 with still functioning cat.