I am with a county government, and being an ESRI and Laserfiche shop, we tried implementing geodocs a couple of years ago. That was when they utilized now defunct silverlight and flex apps, and it appears that they now have an html5 app. For what it was, it was pretty neat. The key feature in my mind was that it creates an index between your spatial features and the laserfiche documents, utilizing laserfiche metadata to do so.
Unfortunately, the project never really took off for us. The department that we set it up for doesn't do much in terms of laserfiche organization, so the search results that the app was returning weren't particularly useful. This was not a fault of the app though, just poor LF organization.
As I'm typing this of course, we are looking at giving geodocs or some kind of custom integration between GIS and LF another go. These things never die...
EDIT: And to your point on it only using AGOL, when we set it up, it did not use AGOL at all. We had a REST service setup on our ArcGIS Server that it utilized, and then weblink on the LF end. Looking through their sparse documentation on their website, that portion does not appear to have changed.