thought the rest of the alarm should work fine even without the powersounder? Seems that powersounders are only found on uk vehicles. In Norway atleast we have the standard Omega alarm but no powersounder. But maybe its a difference in the software or something in powersounder fitted vehicles. Just my thoughts this...
It should, in that, if a faulty power sounder is completely removed and the wires insulated it won't constantly alarm. The alarm / central locking will log a fault code because it can't talk to the power sounder and then give up. It is also true that the power sounder wasn't fitted in some markets but in this case the variant coding on the main alarm / central locking ECU is set to ignore it.
A failing power sounder can trigger the main alarm, as can any number of other circuits. Favourites are the bonnet sensor (just unplug the switch and see if the alarm still activates) and the rear screen protection on estates.
Failing that, a chat with a Tech 2 will reveal the cause of the alarm events. It sounds like the alarm horn has also failed as there should be a serious din accompanying the flashing lights.

Kevin