For a few decades now, admission offices around the country have been processing applications and filing all the supplements (required and completely superfluous alike) that come along with them. Everything was paper "back in the day" (and by that, I mean 2006) and an entire room of our office was dedicated to keeping track of of the paper.
Applications got file folders. Anything that arrived before an application got filed in miscellaneous credential files. Each time an application arrived, staff members would go through the credential files to match supplements with applications. This process was used at every school at which I have been employed. It worked quite well.
With the implementation of paperless admission processes, all of those physical files are gone, but the process remains, albeit with a few changes. When credentials arrive before your application, they still get filed, but they get filed electronically. Ideally, the items coming from your school would come electronically, though the Common App's counselor and teacher portals. If something comes in the physical mail, it has to be opened, have staples and any special packaging (folders, binders, etc) removed, then scanned into our paperless system, and manually labeled with your information and the document type (transcript, recommendation, etc.). Items that come in through the Common App's system already have all of that information embedded in the electronic files, so our system can automatically file them.
The testing agencies have been sending scores electronically for years. Scores show up almost daily and they just sit in the system until there's an application.
One thing that we've have to deal with since going paperless is, surprisingly, MORE paper! For some reason, despite getting confirmation that an electronic item has been submitted to us, people are sending us paper duplicates. Some applicants fill out the Common App online, but print it out and mail it to us. Others send us elaborate supplements (and I'm not talking about the portfolios submitted by students who are going to study performing or visual arts). Please help us out! We are a relatively small office and all of this extra paper slows down the process.
Remember that colleges ask for what they need to make an admission decision and they will provide a vehicle for you to submit that information. You don't need to submit complex extras. This process is complicated enough without worrying about those sorts of things!