Bitcoin existence will always be there, but since its selling and buying transactions will be stopped for a while, then expect that bitcoin promotion will be slow in progress. Even in other aspects that rely on internet, survival is there but there will be slow progress once internet connection will be compromised.

However, things like this will be very unlikely to happen not just for bitcoin, but even in other aspects that are solely operated by the internet. The government itself will surely find it hard to operate if the internet will be lost and compromised.