The Big Picture on Steam has an option to configure controllers. I want to know if I can use it to configure a non-Steam controller?
The Steam Configurator supports Steam, PlayStation 4 Dual Shock, Xbox 360, Xbox One and all generic X-Input controllers.
No, you have to configure it in the system, Steam should automatically recognize the controllers when the appropriate drivers are installed and a game pad is plugged in.
(if you have an Xbox 360 controller and the drivers wasn't automatically installed and you're running Windows 8.1 or later, Open Device Manager, Find your controller (usually under Unknown Devices, try selecting one, unplug the controller and if it was the controller it'll go white again, or stay blue if it wasn't the controller) then right click, Update Device Drivers, Browse my computer, Let me pick from a list, Scroll to the bottom and select "Xbox 360 Peripherals, Next, Select your configuration, then next, and it should show up in steam)