It might surprise you to learn how much of your heard-earned gas money goes through your engine without getting burned. Engines require a good dose of excess fuel to keep internal parts cool and keep the flame front burning. A catalytic converter deals with the extra fuel that comes out, and uses it to dispose of some fairly nasty pollutants.
A catalytic converter is effectively a furnace that burns excess fuel coming from the engine, and then uses the heat from that burn -- around 800 to 1,000 degrees -- to convert nasty carbon monoxide oxides of nitrogen to nitrogen gas and CO2. Like the engine itself, a catalytic converter is tuned to work best when it's running at a certain air-fuel ratio. If you drown the catalytic converter in unburned fuel, it will run out of oxygen and the fire inside will go out. That's likely to happen when you have one or more spark plugs malfunctioning. Fuel goes into the engine, but comes out without getting burned. That excess fuel goes into the converter, and the converter stops working.
Manufacturers learned to counter this effect by installing secondary air pumps to push more oxygen into the exhaust. Vehicles equipped with such pumps are far less likely to encounter converter problems when the engine misfires or runs excessively rich. Some modern engines still use these systems, but computer controls have allowed engineers to detect a cylinder misfire and adjust air-fuel ratio accordingly. Most can adjust and keep the converter working to a point, but a completely dead cylinder can overwhelm its adjustment abilities.
So, long story short: Yes, a bad plug can affect the converter by sending too much fuel through the exhaust. How much it affects the converter depends on how the control computer is tuned, and whether or not the engine uses a secondary air pump.
