Cordless phones I could understand. But security systems?
The phone line actually typically carries its own power, so cutting the main power out won't necessarily affect it. As you said, cordless phones will likely be affected.
Security systems, it depends on whether they have batteries, and also how they're set up to communicate. The wi-fi will most likely be down when the power's out, so if the security system is wi-fi connected it won't work.