If it's RedCare, everyone knows when the line is cut. RedCare is out-of-band signals on a standard telephone line (a bit like adding ADSL Broadband). The ARC's scanner will show up the fault and the STU in the intruder alarm will generate a Line Fault output.
If it's a digital communicator (digi), the intruder alarm should see the line fault but the ARC will have no idea. Recent systems require the alarm to send a test call on the digi to the ARC (BSIA Form 175) so they should notice when they don't get one. But this could be upto 24 hours after the line is cut.
Sorry Bernard, the ARCs (that we use) don't check the lines to digi customers. And NO, they don't know the difference between a line fault and BT engineering work!
We've had many a customer whose been called a stupid-o'clock to be told that there's a line fault 'cos BT are pulling wires out. This includes RedCare connections.
If it's a speech dialler or similar, it will will depend on the unit and how it's been wired.
In any case, if there is no signal to the ARC before the line is cut, only the keyholders will be called by the ARC. If there is an INTRUDER signal followed by a line fault (RedCare), it will be policed (as a confirmed alarm).
At least, that's my understanding of it.