Thank you for your response. Are you able to direct me to where there may online material or basic research indicating or supporting this could be the case, specifically related to the nerve only being intermittently stimulated during pitch response?
The problem is that stimulation of the vagus nerve drops the heart rate and diminishes flow and circulation. In general, this is not helping overall blood flow. There are vast genetic differences in the sensitivity of the vagus nerve, as well as the sensitivity at various points close to surfaces of the body. The late Jackie Kennedy had a sensitive vagus nerve, and was prone to fainting.
For most people, singing of any sort has little effect on vagus stimulation. Coughing, of course does. While vagal stimulation may affect pitch, the nerve is usually only intermittantly stimulated.