I've found that books that are listed on the I'm Reading list as 'NEW', will eventually vanish from that list if you don't open them. You can force this behavior by plugging in the USB cable, and then disconnecting it again. Any ebooks that are NEW and unopened will get filed away into your bookshelf. (This MIGHT not happen with books directly from the Kobo store, as I only have experience with regular epubs I just drag onto the Kobo through file manager.
What I'm wondering is - if I download the epub versions of these books (so far I've only purchased from the Kobo store) and store them in ADE, can I manage this better? Again, I haven't done much more than download ADE because I was using the Kobo desktop program, so I don't really know what's possible. But, theoretically, could I manually move epub files between ADE and the reader? Storing the epubs on my computer once I'm done reading them?
The simple answer to this is yes. You should be aware, however, that these epubs (even the "free" ones from Kobo) are still wrapped in adobe DRM, so you'll either have to abide by the limitation that comes with that, or strip the DRM (pm me if you want to know more about this, there are simply 1-click methods). But even with DRM, the epubs are stored locally when you load them into ADE.
In fact, until we see an update, I would suggest you use ADE to load books from the Kobo store, and avoid the Kobo 'Sync' function altogether. There are some serious flaws with the 'Sync' in the desktop app: it ALWAYS resets your I'm Reading list so finished books become new again, and you lose your place in ones that are open.
I also encourage you to take a look at the sweet little ebook program called "Calibre". If you do decide to take your purchased books and strip the DRM, managing your epub library with Calibre is a breeze.