This would require information that Lansweeper simply doesn't scan. Lansweeper can scan files, but you need to be able to tell it exactly what file to scan, it cannot search for files or file types. It also cannot scan folder information. To do this type of thing you would need a different way of collecting the information.
Personally I would likely write a script to scan this information and write it to the registry so that Lansweeper could collect the information. But that's a bit of a process.
However, speaking on just the technical side of the question, 120GB is far, FAR, to small for 1600 computer/users worth of documents. Storage is cheap, and explaining to users time after time that they have to keep their network folders clean is time consuming and therefor expensive; not to mention pretty much impossibly frustrating for both you and the user. If you're talking 120GB per user, that's more than adequate.
Take this with a grain of salt since I have no idea what documents your users store, but in my experience users have no concept of storage space or what a file size is. This is why you will find 5GB PowerPoints with 10 - 500mb images in them with resolutions of 4000x3000 (but resized to 100x75 so they can fit all 10 on 1 slide). I would make an argument for at least 2 - 4 TB.
-Kris