No, they can't understand each other, especially when they meet for the first time, because the Northern accent is stronger and heavier than the Southern accent. Furthermore, some things have different names, such as:
Bowl: chén (South); bát (North)
Ladle: cái vá (south); cái môi or cái muôi (North)
A glass of ice: tẩy đá or ly đá (South); ly đá (North)