Yes: this puts the Danish/German border into the broader German context. It is useful to be reminded of the boost that the 1864 conquest gave to emigration: much of it westward across the North Sea and the Atlantic, but some also northward into (what remained of) Denmark.
Another important effect was the sharper definition of Danish culture and the boost to Grundtvig's ideas for education and the church (including all his hymns), the folk high schools, the co-operative movement, agricultural development of the heathland of western Jutland, and later the infrastructure of railways, ferries and bridges.
Alastair Thomas