Cutting the phone line externally would not trigger the alarm. The alarm would act as normal and be triggered as soon as they attempt to enter the property. As you correctly say, cutting the phone line would prevent you being notified.
It is possible to eliminate this problem by opting for a GSM Alarm. Rather than using your traditional phone line, the alarm uses a pay as you go SIM card to notify you when the alarm is triggered. The
ERA Vault - Wireless SmartPhone Alarm is a similarly priced model offering this feature.
Phil R