At least on the 97 model year, air pump function is tested by turning it on and watching for front O2 sensor voltage to drop. On my C280 and SL320 it is done at the first stop / idle after the engine is warmed up. ( You must sit idle for about 5 seconds. )

Cat mon looks at the rear O2 sensor. There are some capacitor / resistor foolers for weak cats that sort of work but you must move values around. The resistor lowers O2 signal voltage and the cap smooths the signal out.