Nah, there will be a reason to fight eventually. Whether it's just general antagonism or anything specific is another question.
One thing to keep in mind is that Russia has an aliance whith Prussia and is still angry at austrea for the Crimean war, if austrea declare war on Prussia, Russia will fecal war on austrea, sparking a European wide war that nobody wanted.
France, Austria, Italy and Denmark vs Germany (southern states might switch sides) and Russia sounds interesting.
For one thing Italy is much more likely to sit things out becuse of rome and the bad blood that created woulnt go away Intel the 1880s, and austreas army is still in a very bad state from 1866 and becuse napolion did nothing to actually form an alliance whith austrea (his prime minister was no joke from the "good things come to those that wait" camp that the last bourbon kings prime minister was from) the austrean army was in really no shape to join France at the beging of the war, how it was now I don't know but it will be split in two sence they have to fight Russia as well.Isn't Russia very behind in term of Railway? If so, it's going to be war of the 3rd coalition bis except that this time North German Federation is Austria: The Prussian are going to get rekt before they can even connect their force with the Russians.