Ok - you're thinking of the key as a single all functioning unit.
Think of the key has having two entirely separate functions. It relates to two entirely separate systems.
The alarms these cars have are known as a Cat2+1. That means you have a category 2 alarm unit and a separate category 1 immobiliser unit. Stand alone systems on the car. This is as opposed to a cat1 system that is an all in one job.
So in theory you could, if you had the immobiliser chip, break into the car, start it and drive off with the alarm blaring out as they're not directly connected.
The best thing you can do, if you've got the appropriate level of MultiECUScan, is using an elm cable, take a look at the alarm module on the car and it will tell you how many remotes you've got programmed.
My 147 for example came with two keys, both run and start the car, they even both unlock the doors [manually], just fine, however on looking the alarm is clear it only has one remote programmed, so the second key is never going to arm / disarm the alarm (which can also trigger central locking).
If you want to programme the remote (NOT the immobiliser, just the remote to the alarm) you need the correct code for this, which you should be able to purchase via Alfa, you need BOTH keys present and you can follow the program sequence in MultiECUScan.
You programme the car to accept the keys not the keys to accept the car, therefore when reprogramming as a safety feature it will remove all previous keys and only reprogram the keys that you have with you at the time of programming, so no one else can run off with your motor.
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso