On my test server, while attempting to upload about ten .odc files to the Trusted Data Connection library in Project Server 2013's business intelligence center, I came across this message:
I quickly found the explanation of the behavior here: http://blogs.technet.com/b/seanearp/archive/2010/07/08/your-client-does-not-support-opening-this-list-with-windows-explorer.aspx
And the fix here: http://technet.microsoft.com/en-us/library/cc772567.aspx
This DOES require a reboot.