It's possible, but my profile is set to "Share with everyone" and I still got a notification a few weeks ago asking me whether I wanted to change mine back to "Share only with friends", so I wouldn't assume the worst.
Mine was set to public, too, and I didn't actually realize it because it had been so long (a couple years?) since I had posted anything. When I was editing a post, I was prompted to review the settings ... and I changed it to "friends only". I appreciated the notification.