Cars that sit for a long time can have all sorts of interesting things happen. Mice and insects can chew up upholstery and wiring, build nests in places that cause a problem, like in the ductwork, or exhaust, etc.
Anyway, looking at it from the other side of the mixture, maybe there's a partially plugged cat (or a restriction of something ELSE in the exhaust system ahead of the cat) combined with too much partially unburned gas making it through the cylinders and into the exhaust, and it's continuing to burn there in quantity instead of in the cylinders or the cat, raising the temperature in that part of the exhaust system to a higher level than "normal". If so, I would think that the plugs could just as well be showing evidence of a too RICH running condition.
When a cat is partially plugged, the cat, (which is supposed to run at a fairly high temperature normally), is no longer able to be sufficiently cooled by the now lessened amount of air able to be flowing through it quickly enough to carry the "normal" amount of heat with it, instead allowing additional heat to be transferred to a smaller area of the entire exhaust system by remaining longer than "normal" inside the cat and maybe even backing up closer to the exhaust manifold, in the header pipe and exhaust pipes.
Removing an air pump CAN make a cat be much more liable to plug up-eventually, and usually does IF an engine is run long enough under those conditions. Many things can work to improve performance over the short term, yet cause other problems or cause problem later on. There ain't no free lunch, sooner or later, SOMEBODY pays.
When an air pump is removed from a system with a cat still present, the volume of relatively clean air being fed into the exhaust is diminished, while the unburned hydrocarbons making it to that point are not. This results in less than optimal conditions for the complete combustion of any residual hydrocarbons still present while passing through the cat. With incomplete combustion, there will be, as a minimum, sooty accumulations building up, and there is also likely to be a crustier type of buildup, both similar to what forms on spark plugs over time when presented with a too rich mixture of gas to air or when having to handle excessive oil in addition to a proper fuel to air mix coming from the carb.
Looking at it from the best case scenario, if the fuel air mixture provided by the carb is relatively close to optimal much of the time, and the ignition system is working close to optimally muchof the time also, it may take quite a long time to cause a problem, as there will be a fairly small amount of unburned hydrocarbons actually reaching the cat, so any buildup from incomplete combustion would be likely to take a long time to compromise the cats' performance. Obviously, the farther from optimal the mixture is, and the less efficient the ignition system is, the sooner the problem would tend to start becoming serious enough to be noticeable.
I had one partially plugged cat (on a very cheap, just acquired car) and it was running so hot that nearly the entire cat itself was able to be glowing orange/red with the engine being run for only a very short time. On that one, it turned out that there was a slow coolant leak as well as the slow internal oil usage from the engine both going into the exhaust and over time there was a build up of carbon on the honeycombing of the cat that gradually diminished it's capacity to allow air to pass through. Taking the cat off temporarily allowed the slow coolant leakage to be much more apparent as a slightly steamy fog out the exhaust.
On that car, taking the cat off temporarily allowed the slow coolant leakage to be apparent as a slightly steamy fog out the exhaust pipe that the cat had been burning well enough to hide.
(I didn't keep the car, as in the process of disconnecting the cat, I discovered that the car had been stitched together from 2 others-and not that well. From the exterior and interior it was undetectable, but the frame and floor told the story. The body and paint looked fine, so the body shop evidently did a good job on that part of the job. I've been closely inspecting car frames and unibody support structures on any prospective cars ever since.)
It's not uncommon to hear of someone getting better mileage when a car with an early clean air system, (mainly comprised of just an EGR, air pump, and cat) is circumvented. Without the drag from the air pump, ANY engine's performance should improve. If the carburetor is not subsequently readjusted, the engine is then being presented with a cooler, denser, easier to ignite mixture, so performance may also improve significantly from that. However, the exhaust is tremendously dirtier when this type of removal is done and the car will not be allowed in most states to even be tested to find out if it will pass a clean air test in such an altered condition.
