Not realistic at all. Remember that the internet was designed by the US military to ensure that communications couldn't be taken out by a single point of failure or even multiple points of failure. The packets of information just re-route from node to node till they get to the recipient, even if they have to go the long-winded way around the world to do so.

So say someone cut the cables going across the Atlantic. The info would then route through the Mediterranean into the Red Sea, into the Indian Ocean into the Pacific Ocean and get to America that way. To criple that system you would have to cut all teh cables and assume that govts won't be able to fix the cables as fast as you can cut them.

The bigger threat is lack of electricity - but again, because countries regard this as a core feature, they will defend their electricity generation at all costs. Even Venezuela still has electricity.