Connecting External Lists to Outlook: Tips and Warnings
Applies to: SharePoint Server 2010
To be able to see the Connect to Outlook button on the SharePoint Ribbon and to take an external list offline to Microsoft Outlook, these two conditions must be true for the external content type:
Offline Sync must be enabled.
The Office Item Type field must be set to the one of the Office item types – Contact, Appointment, Task or Post.