Catalytic Converter

This is for comparison of how small the holes on the stock catalytic converter really are. 

There are two catalytic converters on the RX-7. 

The first is a pre-cat, which is the first thing exhaust gases meet after leaving the turbocharger.  This converter is prone to failure due to the high heat conditions and is commonly replaced with a steel downpipe.  Many times, a pre-cat will fail and break into pieces like the one above and clog the main catalytic converter.  This in turn causes immense amount of back pressure which if not treated right away causes engine failure.

The second is called the main cat.  It is the primary source of “filtration.” The air pump, driven off of the belts, pumps fresh air into the converter speeding up the process.  Although this one alone isn’t as troublesome, it is commonly replaced with a mid pipe or a high flow cat.  As soon as this catalytic converter is replaced, the exhaust back pressure is radically different and a tuned or aftermarket ECU is needed to compensate for the sudden increase in flow.  If left untreated, the turbo will have less restriction and in turn, without the proper upgrades, will spool uncontrollably faster.  This results in boost spikes, uncontrolled increases in the amount of air pressure given from the turbos.

Most who live in states where smog tests and emission tests are required chose the high flow cat because it does still operate as needed. 

Ever wonder how people with aftermarket accessories shoot flames out of their tail pipe?  Reason is a combination of a mid pipe and down pipe results in a free flowing exhaust.  The rotary engine by design actually passes fuel straight from the intake to the exhaust without being combusted.  When this fuel is subjected to the high EGTs (Exhaust Gas Temperature) it is ignited.  The result is combustion right out the cat back.

Tim McCreary (RX7Club.com post)

Here is why a catalytic converter is installed in a car:

Three-way cats are to take care of the three harmful compounds. The reason that the air is injected in the middle of the cat is to provide oxygen to finish the catalyst conversion of Carbon Monoxide to Carbon Dioxide and to “burn” unburned hydrocarbons safely without an actual flame or explosion. Without the air pump, you will not complete this process properly. Eventually, you will generate heat or buildup that will either overheat and deteriorate the ceramic honeycomb creating failure and blockage or will generate buildup creating blockage and failure. The following is a description of what a catalytic converter does:
A catalytic converter is a device that uses a catalyst to convert three harmful compounds in car exhaust into harmless compounds.
The three harmful compounds are:
Hydrocarbons (in the form of unburned gasoline) Carbon monoxide (formed by the combustion of gasoline) Nitrogen oxides (created when the heat in the engine forces nitrogen in the air to combine with oxygen)
Carbon monoxide is a poison for any air-breathing animal. Nitrogen oxides lead to smog and acid rain, and hydrocarbons produce smog. In a catalytic converter, the catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe. The catalyst helps to convert carbon monoxide into carbon dioxide (NEEDS OXYGEN). It converts the hydrocarbons into carbon dioxide and water (NEEDS OXYGEN). It also converts the nitrogen oxides back into nitrogen and oxygen (GENERATES SMALL AMOUNTS OF OXYGEN).
My comments are in capital letters in parentheses. As you can see, without an air pump, you cannot complete the reactions necessary to clean the air. Also, if you had enough Oxygen to complete these without the aid of an airpump, you would be running lean and we all know what that means to a rotary.
The reason it is important to put a cat on a rotary engine is due to it’s design. The reason they moved the exhaust port to the side in the RX8 is because the unburned hydrocarbons are just wiped out to the exhaust by the apex seal. The Renesis engine eliminated this from happening which increased fuel economy by 35% and decreased emissions by 50%. Someone else hit it on the head why the precat was installed (to meet emissions because the engine was an emissions hog).
Back to the original question: Does the High Flow Cat clog without an air pump. The answer would be YES. Defining the “Clog” in a cat would be anything that would help deteriorate the interior of the cat to the point that the ceramic would break down and eventually block the flow. Any Cat will clog over time without an air pump. How long? That depends. It may last a few months or a few years. The question I would ask is why spend the money on a High Flow Cat when you can put a straight pipe on for much less. If the answer is emissions, then fix it right and help save the environment a bit so we can continue to run our emission hogs.
Remember also, without the air injected into the cat, the Cat will achieve much higher temperatures than with the air. These higher temperatures will lead to premature failure of the ceramics and eventually clog the cat flow.
High Flow Cats are much less likely to clog compared to the older bead type (highly restrictive and usually melted the beads together due to high heat and close contact). There are High Flow Cats that produce the same back pressure as the straight pipe (Random Technologies had an independent study done on an RX7 with their High Flow Cat and a straight pipe and found the same back pressure).

Actually the cat will heat up, not run cooler because there is more fuel to react with the available oxygen in the exhaust stream. After reading up a bit, there is sufficient evidence to describe two different cats: Three-way and Three-way plus injection. The ones most commonly used on American cars are three-way plus injection where additional oxygen is injected in the middle of the three-way cat after the first stage which breaks down NOx and released oxygen, second stage combines CO and O2 and burns unburned hydrocarbons by reacting with Oxygen. The last part of the cat, air is injected in the stream to allow more complete combustion of any unburned hydrocarbons and conversion of CO to CO2 that may be missed in the first two parts of the cat.
So to change my stand on the original question, yes you can run without the Air pump provided you have the correct cat (three-way that does not require air injection) and a proper working O2 sensor. If you remove the O2 sensor, then the density of oxygen in the exhaust stream is reduced (rich running) and the cat will eventually fail.
To understand why the cat heats up more with less oxygen, understand that the cat is a very efficient tool to make the chemical conversions asked of it. If you remove oxygen injection from the equation, the resulting fuel will still be consumed by whatever oxygen is in the air stream. Without the air injection (78% nitrogen which helps cool the cat), the cat cannot cool down as much, therefore will run much hotter and self destruct if temperatures reach high enough. As temperatures increase, the efficiency of the reaction increases, utilizing even more of the minimal oxygen in the exhaust stream, propagating the process.
The Hydrocarbon molecule is made up of many carbon and hydrogen atoms requiring greater catalytic action and therefore much greater thermal output. So reducing the air injection will actually increase the temperature inside the cat based on the fact that all of the fuel will be converted whether the air pump is on or off, but as excess fuel is sent downstream, there is no air injection to cool the cat down, so it builds up heat quickly eventually failing.

Tim McCreary (RX7Club.com post)