I have the same system and have no problem with the idea that my phone lines can be cut because my in-house alarm is extremely loud and will alert me or my husband the moment anything is amiss. At which point we will retrieve our guns and defend our home and children (alerting the authorities at the first possible chance). If you think that the police will ever get there in time to actually defend you or your family from an intruder, you are sorely mistaken. Police response time varies depending on your area, but even the best you can hope for wouldn't be under 10-15 minutes. A LOT can happen in that amount of time and the police would get there just in time to clean up the mess and file a report about it.
If you're concerned about what happens to your home when you're not in it, that might be another story. But a good, LOUD alarm should be enough to scare most daytime burgalers away. At night? It's nobody's responsibility but your own to defend yourself. You simply can't count on emergency response to get there in time and miraculously save the day.
I have noticed that even though my brother and I both got ADT in our respective homes, my provider installed an extremely loud alarm in the upstairs air conditioning return while my brother's just has a keypad that beeps. So instead of paying out the money for the wireless signal, make a call to your alarm company and insist that they make the alarm ITSELF an actual deterrent...which is the way it should be.