Hi Steve,
If I am not mistaken, web map settings like layers being turned on or off and extent of the map can only be saved in the web map (arcgis online/ portal). Where when you save using Web AppBuilder, you are saving the widgets that will be used, the theme, colors, logos, yadda yadda. So therefore, saves inside of Web AppBuilder will not affect layer visiblity when running the application in the future.
At least, that is the impression that I get.
-Nat