hi
im not sure on BritishBullDog's Clifford alarm, but I know mine has a 2 stage immobiliser. the standard type one that disables the electrics via the ECU, and a 2nd unit that cuts the fuel unless the system is fully functional. you could rip out my system(if you can find it ;-)) but the car still wouldn't move unless they pushed it away.
If they did find the system or ripped out the battery the alarm has its own supply and starts blarring out a lovely sound thatll give you a headache in a few mins hehe.