I just checked it. Your post is still showing up for anyone that hasn't already read it.
When you click "New Posts" shown below, you are actually seeing unread posts only. If you stay logged in, they dim once viewed. Once you logout and back in, you'll no longer see any posts you've already read on that screen.
There is an option to see all recent posts, even the ones you have already read. Once you're on the New Posts page, you can see a Recent Posts link in the pic below, off to the right of the screen. Click that, and you'll see all recent posts, read or not.