Desktop 10.2.1 can create a new GeoPackage, and import data into, but it appears it does not support editing (unless I'm doing something wrong). Does (or will) ArcMap support editing the new GeoPackage data format?
Currently in ArcGIS Desktop, GeoPackage editing is supported via code. You can open an update or insert cursor and update data using ArcObjects. Edit sessions will be supported in a later release.
Runtime will support GeoPackaging editing as part of the summer release.