You're probably going to see a lot of excited posts about Private HOAs now being possible. In fact they have been available since December '13/January '14.
What is new is that if you drop public from the Audience you can create a scheduled HOA that will create an unlisted YouTube video.
Till now this functionality has been available via YouTube so the exciting part isn't that it's available, but that it is now available via the SHOAE form. (blue button ➤ http://goo.gl/eXEBvU)
Remember that there is a live video stream involved in a HOA.
A private HOA secures that stream. Unlisted does not.
This event form was created using the technique for making an unlisted video (http://goo.gl/XoxUdk). The video is unlisted but you can watch it right? This means that if you create an event this way, anyone with access to the event page URL or YouTube URL can watch the unlisted video at any time, even during the live broadcast.
Note that you can view that event form in a browser that isn't even logged into G+ using the "Event Page" link. Not very private at all, is it?
If that isn't what you want then you might want to look into setting up a private HOA instead.
Watch this video for a more detailed explanation:
Google Plus Tips unlisted vs private YouTube HOA