Edit: I misread the app discription. I see it only turns the screen on for a quick moment. Disregard the below
The problem with this app is that the Nexus 5 does not have an AMOLED screen. With an AMOLED screen, the only power used is the ones for the pixels in the notification. With the IPS LCD screen that the Nexus 5 has, even displaying a completely black screen (when the screen is on) WILL use the same amount of power as if the entire screen was lit up white. The backlight is ALWAYS on when the screen is on.