Graphics made with the draw toolbar in an mxd are dropped when publishing to an online webmap. However, they are analogous to map notes in a web map.
Graphics should be automatically converted to map notes when publishing from desktop. This way, one does not have to create them twice (as graphics in desktop and as map notes online), or convert to a feature class instead (and publish them as hosted features - the current workaround if you want them to only be managed from one location).
