Between two servers yes (just use any regular file-transfer mechanism such as ftp, webdav, sshfs, etc). Between two clients obviously not as that defeats all sorts of browser security. You can't even do that with flash I believe.
Maybe in the future there might be some kind of mechanism to establish a connection between browsers directly, but you've got to remember that HTML was created as a client/server architecture & all features pretty much assume this behaviour.
If you want to transfer files directly between users, then webapps are the wrong tool. Especially with big apps, use something like Bittorrent instead.