Although this review is of a C350 Coupe it is I believe the same system on mine.
From Car and Driver:
...the new C coupe offers an optional—special order, only—sport suspension package called Dynamic Handling. It lowers the body by 0.6 inch and stiffens the springs and dampers. The advantage is agile handling in sport mode, even as the system softens up midflight if it encounters crummy roads; the transition happens in as little as 10 milliseconds. The handling package also includes a stability-control-based torque-vectoring system. In fast corners at the adhesion limit, when the stability-control sensors detect encroaching understeer, the system slows the inside rear wheel in order to assist the yawing moment. As a result, the C coupe turns into corners with precise control and real determination.
This summary was from a MB reference:
"With the continuously variable damping, handling becomes more taut, body roll is reduced and the ride becomes firmer. Steering and throttle response becomes sharper and gear changes more responsive (automatic transmission only). Even ESP® (Electronic Stability Program) intervention is marginally reduced to help enhance the dynamic driving sensation – without compromising active safety, of course."
So, the height reduction is permanent (when compared to a car without the Dynamic Handling Package), not when the Sport button is pressed.
I have never heard of a car with variable dampers also lowering ride height .. that tends to be for cars with more complicated air/hydraulic/etc suspensions.