I know I'm a little late here but I just started looking in to this.
From my understanding,
You can upload your own layers, mxd, layer packages, ect. However, once you share them users will only be able to download them and use them in ArcDesktop, not ArcGIS.com. If you want to be able to use and share your ArcMap files, you need an ArcServer (not free) in order to do so.
-Amber