When the throttle plate closes, there's suddenly a bunch of air pressure "piling up" in front of it, and a "big vacuum" behind it. The BOV is opened when a "big vacuum" condition occurs, and eventually springs back shut when all the "piled up" air pressure is gone.

This is why most aftermarket BOVs have an adjustment screw, to control exactly when the BOV opens. Typically you adjust the BOV to just barely shut at idle -20inhg or so.

If the engine isn't running there is 0psi in the manifold, and the BOV will be VERY closed. You would have to use a vacuum pump to get it to open during a boost leak test.

Feel free to slam me if I'm wrong, that's how I understand it so far.