It looks like mobile geodatabases aren't supported in ArcGIS Online.
What can you add to ArcGIS Online?
As far as I can tell, I would need to copy the mobile geodatabase data to a different filetype like a file geodatabase, and then zip the file geodatabase and upload it that way, which seems backwards. This is where GIS people get into trouble: too many copies of data.
It would be great if ArcGIS Online could be enhanced so that we could upload data directly from a mobile geodatabase.