I've tested this using a SharePoint 2007 instance with the same results...
EDIT: Also, Page Files, Global Files and Documents all work correctly.
I am having the same issue on SharePoint Connector 2.4 (CMS 6 R2 against SharePoint 2010). Did you figure out what was causing this?
I've just installed a fresh EPiServer 6.0 website with Public Templates and then installed SharePoint Connect 2.2 on the website.
When I go to the File Manager within the Admin Mode of the new website and click "SharePoint" the error "No registered virtual path providers are accessible" is displayed.
Also, browsing to the SharePoint folder using the File Manager within the Edit Mode strangely shows the "Unsaved page" message. Clicking OK doesn't do anything.
I am using SharePoint Server 2010, but from what the install notes say, the connector is fully compatible.
I have deleted the website and re-installed from scratch with the same result.
Has anyone got an idea why I am having this issue? I've had a scan around the config files and have not noticed anything missing.