The purpose of the EGR is not to reduce unburned hydrocarbons. Instead it is designed to reduce NOX formation by reducing high temperature situations. It does that by recirculation burned exhaust gases back into the combustion chamber. These gases then act as a diluent which in turn lowers the combustion temperature.

That being said I don't know the answer to the original question. My guess is that the solenoid is energized stictly under computer sensor control. The valve will open in varying engine conditions thus the vacuum it sees will vary but will primarily be during high load (i.e. high temperature situations).