Margaret, Gary,
You should be fine if you just save the web map.
For your edification, the reason someone might choose to save the drawing and popup properties back to the feature layer is so that when it is subsequently added to different web maps, it will have that information already, rather than having to define it for each web map. This workflow currently is best suited to hosted feature layers that are updated through Arcgis Onlne's editing tools, rather than externally.
Mike