Yes and no. German people did begin to address national questions of identity and unification starting with their defeat to Napoleon. Germany was, however, culturally and politically fractured even after unification in 1871. While it would have been accurate for some to say in 1860, “I am German,” as evidenced by unification efforts in 1848 and the continued discussion of the “German Question” into the 1860s, there were still strong cultural ties to individual states. To have an identity with Prussia, Bavaria, or even Austria, was not uncommon, the result of which was to create a problem for Germans in deciding what a unified Germany would look like.

By 1858, public opinion had moved past the question of “should Germany unify?” to “How should Germany unify?” The factional nature of German identity became very clear in the years before the Unification Wars. There became of the problem of who should be included in Germany. Should a unified Germany, Big Germany, include Austria, a 70 million person multi-national empire? Should a Little Germany include Prussia, a nation with a newly reformed military that would dominate in the place of an excluded Austria? Or should neither be included, and a Third Germany be created that would likely be dominated by Bavaria?

The Little Germany solution eventually won out for various reasons, but that’s beside the point. Those state identifications shaped unified Germany. The states in southern Germany were hesitant to join at first, or eventually did so only with concessions that allowed them to maintain some degree of autonomy. Bavaria was even allowed to maintain its own standing army, Württemberg also playing for a privileged position but ultimately failing.

While not directly related to the question, it should be noted that state loyalties continued to play a part in shaping German history even in the years before the Nazis took power. That states could assert their independence from the national government even into the 1920s and 30s attests to the popular support they had separate from Germany as a whole.

Stefan Berger’s “Germany” and Michael Rowe’s “Napoleon and Europe” on Napoleon’s impact on German national discourse.

Alon Confino’s “German Federalism” on national and regional political ties.

Martin Kitchen’s “History of Modern Germany” for broad historical analysis.

tl;dr There was a national identity prior to unification in 1871, but there was also strong cultural loyalty and power within individual states that remained at least somewhat independent of Germany as a whole.