Currently the Atlas app is able to load webmaps in non-Web Mercator projections from a configured Group. (thank you!), and the author can specify which basemap will load when the app is opened (also good!).
However, when attempting to use a non-Web Mercator basemap as the initial map (Advanced Settings -> Atlas -> Change the default basemap) and choosing any non-Web Mercator basemap the chosen map is not displayed — the screen is just blank and there are no errors in the browser console.
It would be nice to be able to show a non-Web Mercator map when the app initializes.