In my 2004 E500 4-Matic wagon I pulled a connector off the rear fuse box.
This disables the alarm siren and tilt alarm. Basically it shuts off power/communication to the siren w/ battery back up unit under the left front fender well. It also then would disable the tilt sensor that detects if your car was being towed without consent.
My parking lights still flash 3 times when locking the wagon and the dash displays a flashing red light between the lock buttons like the alarm system was being armed and I believe it still is. It just won't be able to trigger the siren to chirp three times of sound off it the alarm is set off by a break in.
This does store a code that's stored in the ECM. It does not set off a malfunction indication on the dash display.
I disconnected mine due to the siren unit being defective and blowing the #8, 7.5 amp fuse. This fuse also controls power to the radio antenna amplifier and key-less entry so if you have crappy AM/FM radio reception and your key-less entry only works when you put your key right up to the door handle (IR Control) this fuse is probably blown. The siren unit's NiCD batteries fail and corrode the circuit board after length of time (5 years+)
Eventually I'll get a new siren unit.
Here's the link that shows photos of the actual location of the connector that needs to be removed. I had to swing out the DVD Navigation unit in my wagon to access the connector for removal: