Hi,
I'm not sure why you really want to show that, but you can cache all documents and then with simple LINQ take only published on the live site. Something like code bellow:
var allDocuments = DocumentHelper.GetDocuments().ToArray(); //cache this
And then when you take that from cache, add check for Live Site and do something like:
allDocuments.Where(doc => doc.IsPublished);
Best regards,
Dragoljub