A subverted 1848? Nasty thought, but possible. Though no t as easily as you describe it.
First off, the 1848 constitution was democratic. It would only be the Emperors government in the same sense as Browns government is Her Majestys government, that is de facto not really. The monarchs were to gain a delaying veto, so they could strangle the politcial process to a degree, but nothing more. Hence, the Emperor couldnt simply build up a junker government. Of course, since it are his armies marching what he could do is a coup d'etat. But that wouldnt be a 1848 Germany then of course, but a "Successful German Union (Erfurt Union)" scenario, where the smaller mnarchs follow Prussia out of fear of new revolutions.
And then theres the question wether Russia and Austria will allow that. Germany can easily stand against either of them apart, but taken together... so, a sucessful 1848 in Germany also does require a more successful 1848 in Hungary, to keep both Austria and Russia occupied.
Of course, with an early enough PoD we could have a through and through idealistic liberal Prussian King. Its unlikely, but still probable enough as a PoD. And hey, why shouldnt Germany have a stroke of luck. I mean, at least once. For a change
Another possibility is (again assuming Austria and Russia are occupied in Hungary) a more competent Paulskirche Parliament, who manages to organise a levee en masse against the Prussian interventions and then manages to conquer Prussia. The questions of constitutional law and who gets to be Emperor are still there, then, of course, but with Prussia knocked down it could very well suceed. Ive suggested this possibilkoty twice before, and as then my suggestion for Emperor would be the
House of Meran 
This is of course nozt all that likely, but possible. After all, the French Revolutionary mass armies beat down most of Europe, why shouldnt German revolutionary mass armies be able to do the same to just Prussia?
Btw, the title is indeed "Deutscher Kaiser" (German Emperor, for all the connotatoions it has acquired in English, Kaiser just means Emperor), both in the 1848 constitution and in the 1870 Empire.