I'm surprised that ArcGIS online maps do not act the same way as ArcMap when a layer is turned on but is not visible in the current extent....
ArcMap :The layer is checked but it is greyed out to indicate that is is not drawn
ArcGis Online: The Layer is checked and not greyed out which gives the user the impression that it has drawn.
This could be confusing to the general public when view maps online.
Simple but important idea.. If a layer is checked and it is not visible in the current extent, make the chech box GREY.
Thanks,
Christina