I believe that the monitor is required when running vr. It shows a mirror image of what's on the hmd. Unplugging the monitor will have no effect as the mirror will still be pushed down the monitor output even if the monitor is not plugged in.
Some games do not have a external mirror but they are usually games designed that way.
What you can do though is set the monitor mirror to a low resolution as that should not impact on the HMDs display. Thus minimizing the GPU overhead.