While you can offload the encoding to the NVENC chip on a GPU, what you need to understand is that OBS still uses your CPU to run and handle all the scenes. With the most bare minimum setup of game capture and a webcam you can get by on spare CPU power while gaming depending on what CPU you have and the game you are playing.
Once you start adding overlays, notification gifs, and other effects, CPU usage starts to go up significantly the more you have and the more complex the overlay is (such as using a webm overlay for animation effects) and this isn't good when you are also playing a game that uses a good amount of CPU. So to stream on the same PC you're playing games on requires a lot of CPU power.
And since NVENC is a dedicated chip on the GPU, you don't really need another GPU in your system and can use the 1060 to do it while you play games.