Does using a brightness reducing app save battery?

I installed the app Brightness Slider on my MacBook because the lowest brightness setting in the System Prefs isn't low enough at times. When I choose a brightness setting below what the System Prefs allows, does the laptop in any way actually consume less power? Or is it using up the same amount of power?

You would expect an app that dims the screen to save power. LEDs show a linear relationship for luminous intensity vs. forward current. The more you dim your LED display the less current it consumes.

(I'm assuming you have a LED-backlit display as all current-model MacBook Pros and Thunderbolt Displays are, and I looking at a LED data sheet found at SparkFun for the intensity/current relationship. It should be the same for any LED-based product.)

BUT if the app is not actually dimming - just covering everything with a transparent layer - then it may use more power. That app's reviews suggest it causes the discrete GPU to become active so I don't think there's any way it could be saving you power, more like the opposite. Adding a transparent layer over the entire display may decrease the apparent screen brightness but increase battery consumption due to the GPU having to do more work to blend the transparent dimming layer with other elements on the screen.