The purpose of the Connect to Outlook button is to let the users to display the data from SharePoint Discussion List in the Outlook Calendar.
It doesn't work with OWA.
This is what the documentation says:
If set to true, the Connect to Outlook button will be displayed in the toolbar. The
Connect To Outlook button lets users view their Sharepoint Discussion lists in their
Microsoft Outlook Calendar. The Connect To Outlook button will work only if the user
has Microsoft Outlook installed in their machine and it only works for the SharePoint