From what I understand (at least on my C280) is the radio can be turned on without a key, and will run until the car battery was drained to a certain point. This keeps you from having a dead battery if you accedentally leave the radio on and forget. Same goes for the feature that runs the fan/vents to keep your car warm for a half hour, or if the voltage from the battery drops below a certain point.
1986 190E 186K (For Sale)
(Maroon, Tan leather)
1996 C280 Sport 208K
(Brilliant Silver, Black Leather)
2002 CLK430 Sport 45K
(Brilliant Silver, Gray Leather , Birdseye Maple)