The alarm should set, but the perimeter sensors will be switched off.
If the doors are locking, try unlock them with the key & open - does the alarm go off?
Also, sit in the car & set the alarm, then move around - does the alarm go off?
If yes to either above - problem should be limited to the boot mechanism, and should be fixable diy or local garage
If the doors are not locking as well, may be a system problem and dealer or specialist fix only