I recently updated Wordpress, Laytheme, and Add Ons. In the latest updates, the Carousel Add-on doesn't appear in Preview or on the permalink when the project is set to Private.
It does appear when the page is set to Published with Public or Password Protected set.
I've deactivated other third-party plugins, cleared and disabled my cache plugins, and temporarily removed CSS and JS. None of these affect the Carousels, only the Status and Visibility settings on the project.