I was just too lazy to be specific. I'm guessing that the OP was asking, if you pull the outside door handle when the car doors are locked and the alarm is armed, will the alarm go off if the door does not open because the lock is fully functional? And the answer based on how my car alarm is,is "No." The alarm will go off when the door is actually opened and the alarm has not been disarmed. Just pulling on the handle will not set off the alarm if the door doesn't open.

Some possible scenarios are:
#1 Your passenger is too slow to get out before you get out, close the door and hit the lock on the FOB. Once your passenger opens the door the alarm will go off.
#2 You hit the lock button and your vacuum pump-central locking system is malfunctioning or the air hose in the vacuum pump system is leaking and your locks dont actually lock but the alarm is functioning; awhile later you come back and forget to hit the unlock button and just open the door.
#3 You leave your windows open after getting out, you close the door and hit the lock on the FOB. A stalker that's been following you walks by and reaches in and opens the door.
#4 Car door locked and alarm armed, Superman comes and rips the whole door off of the car will trip the alarm.