There is what I believe to be a misconception that the auxilliary cooling fans are supposed to come on whenever the AC is on, as they do on some other non-MB vehicles. MB took the approach that the aux fans come on only when actually needed. For newer vehicles (starting, I think, in the late '80s) the aux fans have two speeds. Low speed is triggered by high AC pressure and is designed to protect the compressor from excessive refrigerant pressure. High speed fan operation is triggered by high engine coolant temperature and is intended to protect the engine from overheating. In neither circuit is there any provision for the fans to operate just because the AC is on; the other condition must be met for them to come on.
If you do that search now, you can learn more about the two separate circuits and how to test them.