That's a 3G (cellular) modem/router.
As far as I know, no DSL modem/routers have a built-in battery backup. However, you can power most of them from any 12V source, such as a SLA battery with a trickle charger.
Also note that depending on how well maintained your phone network is, it might not stay up for long in a power cut. No use having a battery-backed modem if the DSLAM is down.