My '91 SE has a clutch on the smog pump, just like the AC compressor.
It engages for a couple minutes on cold start, then disengages and just turns the outer idler pulley, not the pump innards.
If you don't want the pump to run, just unplug the wire?? and it freewheels on the idler bearing. If the idler bearing is bad it can be replaced with a std bearing part number as I remember. My pump got a bit noisy about 5 years ago, had the wire unplugged ever since. Has no effect of smog test, as they test it with the engine warm, when the clutch would be disengaged anyway.

Maybe the E-class is different??

DG