I can only see this happening if they allow things like folders within folders from within apps' file interfaces. Without that ability the Finder remains essential for many of us. It would be nice to see Finder go the way of Terminal though.
My android phone has no finder by default, and iOS also comes without, as far as I know. Still people are able to store and access data on their smartphones and iPads. However they stop worrying where that data is actually stored, as long as they remember how to access it.
Also on the desktop it will be beneficial to move away from the "A file is in a folder is in a folder is in a folder" structure. If I open iTunes, I see all my music in a simple, organized way. I don't care that each song is stored in
/Users/username/Music/iTunes/Media/_name of artist_/_name of album_/artist.album.songname.mp3
When I got Lion, I thought "All my files" was the most stupid change they could ever make to Finder. Just right now I figured out how useful it is. I start keynote, click "Open", click "All my files", and immediately have the list of all presentations on my machine, and I can even preview them without opening them.
Right now I still have to worry about my files going into the dropbox folder, for backup purposes. In ML this will be easier, since I can decide to either have it somewhere on my filesystem, or on the cloud. I just hope that there will be a setting to keep a local copy of each cloud file, for when there is no internet.