The risk of a blocked air filter affecting emissions of a modern car is virtually nil thanks to the closed loop system of sensors and other components which keep the engine running at near stoichiometric air/fuel ratio. Manifold pressure, airflow, or both are used to help determine what the mix should be, and the feedback from the lambda sensors confirm that it is correct and that the catalyst is performing correctly.
Holes in the system before/after/between sensors allows air to get in/out where it shouldn't and leads to the ECU compensating by injecting more/less fuel. As an example, taking the lambda sensor out the exhaust and just hovering it in air with the engine running will cause the ECU to significantly overfuel the engine as it thinks it's running incredibly lean. 'Clever' ECUs may even report a fault with the fuelling system in this case as it assumes a blocked/faulty injector.
Stoichiometry is important for catalysts as they will deteriorate rapidly if the fuel was too rich/lean. "Lean burn" technologies as developed by Ford in the late 1980s had to be abandoned by 1992 and (ironically) fuel consumption and compression ratios suffered as a result for a few years.
As emissions have got tighter so the number of sensors has increased. Early emissions legislation was satisfied by only a passive 'open loop' system with the injection system (or carburettor for Rover A-series) set for stoichiometric-ish combustion. As we went through Euro II, III, IV and V a lambda sensor was added before the catalyst, then another after it, then more sensors, fly-by-wire throttles, etc.