Can a countrys dialects differ so much throughout that one may not be able to speak to someone across country?

Ive recently been kinda studying the origins, dialects, histories, etc., of a handful of languages, which have some pretty highly-differing dialects throughout the country of which that language the dialect is from is official. Lets take Dutch for example: If, by chance, a man from Friesland, a northern province of the Netherlands, were to encounter another from Limburg, a far southern province, both of which speaking two different dialects as opposed to the large majority who stick with the official Dutch language, could one mans dialect differ from the others to such a majority they couldn't understand or speak to each other? Because not everyone in the Netherlands speaks Dutch. As goes for any other country with such differing dialects throughout, would the inability to communicate be a possibility?