Upon investigating, it appears there is a bug. It is supposed to send the e-mail via Bcc, but due to the bug it doesn't send it at all. This will be fixed shortly (tonight or tomorrow). Let me know on your next order close date whether it worked or not.
As for the enhancement request, that's a good idea. However, right now there is no easy way for the system to know when your order cycle has opened. It can tell when it closes by the auto-lock date setting, but there is no "auto-open date" setting. The closest trigger is when a source goes from being locked to unlocked.
So really the feature would have to just be tied to the "Unlock order" button. e.g. whenever an admin user unlocks, it would give them an option to send an e-mail notifying all members that the order is open for ordering.