The refresh rate of the monitor just determines the maximum FPS it can show, regardless of the refresh rate of the monitor the GPU is still drawing frames as quick as it can, when you have a 144Hz monitor it will transfer frames from the frame buffer to the screen more often but that is a light task compared to rendering the frames initially, you shouldn't see any degradation, though if you are only able to render the games at 60 FPS increases the refresh rate of the monitor won't gain you anything.