No, it's not like that, blocking internet access would cripple nation states' economies too much to even be able to fight a war. But censorship even without a major war requires centralization of control over the internet, which introduces a country-wide weakness that makes the internet unreliable to the point of complete blackouts, like during anti-government protests. Furthermore even a small conflict has an impact on the supply of electricity in the country which also could make all storage nodes there unavailable for prolonged periods of time. There are a lot of other weaknesses too, like not that many countries even have good global internet connectivity and cyber attacks could shut it down entirely.