Macbook Pro External Monitor Mirroring GPU Performance

Hi. I want to game on an external monitor on my macbook pro early 2015. OS X doesn't have the option to display to external monitor only, and I don't want to run in clamshell for ventilation preferences.

My question is, does mirroring the display tax the gpu? In other words, I want to mirror display, turn down brightness on the retina screen, and play my game on the external, but am wondering if this will adversely affect performance. Using the external monitor as a secondary display most definitely taxes the GPU because it needs to render two separate images. However, it is unclear to me whether just sending the same signal to both screens is also taxing to the GPU.