The compressor should be off when in Economy (EC) mode. Every other function it should be running unless the coil gets cold enough to operate the evaporator temp sensor at which point the compressor starts cycling. The air should never be colder than ~42˚ if the system is working properly.

The microswitch on the accelerator linkage will also drop the compressor out at WOT

The overheat sensor in the head will drop the compressor out when it operates. The trigger point varies on year and model.

The Klima also checks the speed sensor on the compressor and will drop the clutch out if it senses that the compressor has stalled.

The Klima as designed also adds a delay when the engine is started so that the compressor does not engage until 600 RPM is reached.

So the Klima actually does do some important things, but most of the functions can be replaced with simple relays.