You can acutally just setup the desktop to turn back on when the power comes back on (BIOS setting - hit delete when starting up). However usually laptop's can't be setup to power on. So if the power goes out longer than the battery can last, you're in trouble. I'd test the battery life on the laptop, if it is a few years old you might only get 10 minutes or so.
Of course, it would always be nice to be able to text message a cell phone in case of power outage, my computer with a UPS sends an sms message to me if my house power goes out
