You can indeed use Channels as the backbone of a notifications system using WebSockets, but you'll need to overlay your own state logic on top (notably, "what has already been sent to the client?") You can also in theory use Channels 1 to do long-polling, but this is likely going to make a lot more sense once Channels 2 is out and you can write native async HTTP handlers.
Given that not all browsers or corporate networks support WebSockets, I would suggest you first build an AJAX short-polling based solution for maximum compatability (but it's going to strain your servers as more people use it), then add in either long-polling, WebSockets or both as options based on what gives you the best return in terms of UX and development time.
Andrew