Wow - I never noticed that a Converted doc does not have a valid name OR a valid fullName, unless it has been Saved once -- only the filePath is valid! (So a Converted doc behaves pretty much like a New Untitled doc.)
Off-hand, I don't see any other way to get the original doc name of a just-Converted doc.
But why not have the script open the ID CS5 document in ID CS6? ... then you can grab the File or path of the document before it is even open.
You must have a lot of documents to convert anyway, right? Otherwise you wouldn't need a script. So it seems like what you really want is something like a script that converts all of the CS5 documents in a folder to CS6. If so, it is not a very hard script to write, and I'll bet that someone has one already laying around...