The OEM alarm still works by locking the driver's side door or activating it through the keyfob.
Changing the BCM does not effect the operation of the alarm.
Just be sure to get one from another 96 or it won't work. Doesn't matter what engine size or model (Base, Laredo or Limited).
Just remember that your odometer will change to whatever is in the replacement BCM. I was lucky and went from 216k miles down to 156K miles with a $4.00 swap. And, when I lock my doors now with the keyfob, my horn chirps like it's supposed to. My original BCM had that disabled.
I have a lot of recent experience with BCM's. I just changed mine out 3 times trying to fix some issues with wipers not parking or working with the delay and it did not help.
That's a whole other story though and I won't hijack your thread.
Why are you swapping yours out BTW?