Since you've never heard it, I have to assume that it's similar to my '96 E300. I wasn't sure it worked until I set it off by accident while sitting in the car.
Try sitting in the car, and lock the car with the remote. Then open the door. You might want your remote handy to turn it off.
As far as I know all MB alarms arm automatically with remote. When you use mechanical key, it will not arm. Using valet key to open will trigger the alarm, till you insert the key into ignition.