No, they'll continue to feel like that even after that. GitHub being down once in a blue moon is more acceptable to the vast majority of users than having to cobble together your own nerdy distributed version of everything.
Then it'll be up to the nerds who manage to cobble together their own distributed version of everything--even if it's a significantly reduced definition of everything.
Or, if it's a political scenario, it may depend on how well we can coordinate en masse without the cut connection. If we can exceed a certain threshold then we'll have removed the incentive to cut it in the first place.