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No the cloud will work as before.

Before the change you didn't have to be online while playing a game, which means that you couldn't profit from the cloud.
Nothing changed.

Cloud is only helpful in online modes (bigger maps, more players, online stats tracking, better performance etc.) and it's perfectly possible that there are cloud only games that require you to be online (a few multiplayer centric XBLA games already need you to be connected to the internet before you can even start them)