You will notice that when you lock your car with the remote (arming the alarm also), the doors will not open from the outside or the inside. Pulling the inside handle (as many times as you wish) does not engage the door mechanism. Hence this alone will not set off the alarm. However if your motion detector, located on the inside roof in that square do-hickey, is working properly, the alarm should go off when you reach inside to open the handle.
You can get locked inside the car this way also. If you lock the doors with the remote while inside, you cannot open the doors until it is unlocked with the remote. This is one reason BMW tells you to use the lock switch inside the car to lock it when you or anyone else is inside the car.
Also the siren should be LOUD AS HELL when sounding. My X5 which has the same alarm system and siren as your 3-series will break your eardrums if set off inside my garage.
Like codex says, the alarm does not have a shock sensor. Only a motion detector and tilt sensor in case someone tries to tow it away.