Wouldn't that butterfly away the casus belli used to spark the Austro-Prussian War? Granted, war between the two powers seems to have been an inevitability, and I'm sure Bismarck would have been able to conjure up a new reason for war, but that might change the circumstances of the conflict.
Diplomatically, the British are rather pissed off at the Prussians (even more so than they were OTL?) and it might threaten relations with Sweden-Norway for a while.
In the long run, however, assuming that the German Empire is able to form more or less as it did OTL, I expect that Kgr. Danemark would have similar levels of autonomy to Bavaria, with various independent state organs, its own army, and perhaps even its own coastal defense force/navy and merchant marine? I also imagine that trade with the rest of Scandinavia would increase with the addition of Denmark, and in the long run you might even see improved relations between Germany and Sweden and intensified cooperation on defense and security. Britain, however, would be more hostile to Germany and its interests from an earlier date. Having access to naval bases in the Faeroe Islands, Iceland, and Greenland, however, would definitely help when WW1 comes along, and not just from an economic or military standpoint. Control over those land masses would probably break the Entente's near-monopoly on the flow of information and propaganda, which could butterfly away US entry into the war.
Furthermore, having naval bases further north along the Heligoland Bight and maintaining total control over the Skagerrak and the Sound would help immensely with fighting both the Royal Navy and the Imperial Russian Navy.
On the topic of Iceland and the other Danish colonies, I imagine that Iceland might be made a kingdom or grand duchy within the framework of the Empire in order to stifle separatist movements there. The Faeroes, Greenland, and the Virgin Islands will probably remain subdivisions of the Kingdom of Denmark, however.
