I think the "Storage Box" is for TV recording and it states "The two terabyte hard drive" so I'm assuming that it is local storage. However, it says what they will provide web-based management so I assume that it will be accessible from the web (or the "remote" interface). I will assume that the TV box will also be able to read files from Google Drive because it states "All that storage means you can upload your precious family videos and photos for easy access from any of your devices".
I honestly can't see anything bad about this service. The pricing is very cheap. I'm paying around the same price, maybe a little more, and the internet speeds are about 1/40 as fast, and the TV service is lousy. Assuming everything works as expected, I really hope we will see a change from ISPs. They have a tradition of providing ok service, but charging a ton. Google wants to give customers an amazing service, and price reasonably. If only we see a Google Mobile in the future, with the same "No data caps" as the residential service.