The Kompressor works all the time, it's driven off the crank by a belt. I suppose there must be some kind of clutch but, essentially, it will be working whenever the engine is working. That is the advantage of a supercharger over a turbocharger: the latter, being driven by exhaust gases, needs a build up of pressure in the exhaust to spool up.
My mother drives a SLK230k, which has the same engine as your car. My car has the two litre four without supercharger. Her car has a rasp noise, but that may be in the exhaust. There is a definite gruffness from the engine, though.
Her car is also quite free to kick down, although the shift points are a little lower than David lists. Same ball park, though.
1999 SL 500
1993 320 TE
1986 500 SEC