No. Many immigrants to Scandinavia only understand one or two of the three main Scandinavian languages -- and they are usually more likely to flop with western forms of English than native-born Scandinavians, although, even amongst the latter population, I am finding that teenagers and those under 30 are worse in English than 30-50 year olds, a shift from a decade ago in Scandinavia).

Some ethnic majority Scandinavians have trouble with nuances or even numbers in one of the other Scandinavian languages. [I know Swedes who default to English when dealing with Danes over basics like numbers because of misunderstanding/limited understanding issues.]

Written communication is less of an issue than verbal communication across the Scandinavian languages. Drawn out verbal communication easier to understand than rapid-fire, short verbal communication.