I think it is a very good idea.
I like spectating games a lot, as it is a great opportunity to learn or to find a champion that one may like - especially if you are a beginner with just a few, still looking for "your way".
It would be nice if there was a separate tab, just like Store and Profile, for Spectate Live, that would be always available and people who enjoy spectating wouldn't have to be forced to give up that part of LoL, when (just as today) championship happens.
I think Spectate Live has a great potential, and hopefully in the future we could also have an option of searching through streams by a name of a champion i.g. you could type "Lux" and you would see all games with her that you can spectate.
I, along with other spectator mode fans, would be very grateful for considering and hopefully implementing our suggestions.