I created an external content type connected to a SQL table and chose announcements as the office item type.
You need to enable enterprise features on SharePoint. Do this in central administration->upgrade and migration->enable enterprise features. At least that enabled it for me.
Try using SharePoint Designer to edit the Entity you mapped to an announcement.
In my experience SharePoint Designer reports more warnings than a BDC Model import.
There are a number of features that are not supported on an External list since the content is not stored in SharePoint. It would make sense that the Connect to Outlook feature is one that would not be available.