Cutting the phone line does not disarm the alarm. Some alarm panels can be programmed to monitor the phoneline and set off an alarm (sometimes annoying), alarms that don't have the feature built in to the panel a module can be added to do this. However, neither will fix the transmission problem due to the downed phone line.
You can add celemetry type of backup (Uplink) or full cellphone backup. You can't talk on the Uplink. The drawback is that you have to have a wholesale account to install and program these systems. But, your central station will recieve the alarm if the pots line is cut...provided you have cell service in your area.
Soooo...you can buy equipment, install & program it yourself but probably not the long range radio backup.