Nop! It seems that the display of the route layer in the output is completely arbitrary. Sometimes it works, sometimes it doesn't. Maybe it's another bug in the unstable model builder! Both Add to Display and Model Parameter are checked for the output of the solve operation, and still, the route result isn't displayed on the map. I don't know where it hides!
I'm also interested in displaying the results form a network Solve in either a AGO map or a web app. Haven't been successful in either platform. I've put together a python script tool and published as a GP tool for use in a Flex app. It runs and generates a solve layer and directions text file on the ArcGIS Server. How might I leverage this into AGO?
One other thing you can make sure to check is in the ArcMap top menu, click on Geoprocessing and select Geoprocessing options and make sure that the "Add results of geoprocessing operations to the display" is also checked on.
Thanks for the suggestions. I'm able to display the results from the script tool in ArcMap, but no such luck with getting results to display via a geoprocessing service in a flex app. Apparently it's a bug with the Flex api. Now I'm wondering how I might be able to leverage and use a network data set in ArcGIS Online. Any suggestions or ideas?