In the case of a power failure and Internet connection cut (cable or DSL) then you would be dead unless you had (as stated earlier) a UPS. With a UPS you could keep the core on but any IP cameras and USB cameras connected to the MD's would be dead. Most Z-wave PIR's and Door sensors are battery powered and as long as your Z-wave dongle was on the core your Z-wave sensors would work. So the sensing half of the security system would work if you used z-wave.
How do you alert somebody?
With no Phone line neither the conventional or LMCE can make calls out
if you had a conventional alarm, in most cases, it would power up the siren and alert the neighbors even without any sensors being tripped. More advanced ones would wait for a sensor to be tripped but would power up the siren once this happens.
So LinuxMCE would be as good as a conventional system with the addition of a Z-wave siren under these conditions and well in advanced of most when power was on.
I have tried searching for a Z-wave siren and came up with nothing. You could make something if you could find a 6-12v z-wave relay, a regular siren ($15 ish) and a 9v battery. A fun project me thinks