You havent said what signalling system your ADT alarm system is using. If you are using a digital communicator (also known as a dialler or modem) you will still be using an analogue line for ADSL so a filter is fine. You can actually buy a wire in filter so the alarm line cannot be unplugged easily.
If your alarm uses BT RedCare signalling then you might have a problem as Redcare is a BT service and must sit on a BT line free from other data devices unless you use a Modem compatability device or MCD.
Talk Talk will not say they will support it as you will find that BT dont either! This is just a way of covering their backs.
Good luck.
Pezza