There are two historiographic answers to the question of "how democratic was Imperial Germany" and both lay out persuasive points for both a (soft) affirmative and the negative. (Warning: what follows is more of a targeted historiographic survey that hopefully answers the question, so prepare your pillows)

In the postwar 1950s and 60s, the Bielefeld-school led by Hans-Ulrich Wehler painted a coherent picture of Germany’s trajectory towards illiberal dictatorship and racism. Wehler in particular emphasized that Bismarck subverted democratic processes that retarded political development. Termed either Caesarism or Bonapartism by Wehler, he argued Imperial Germany's executive branch (both the Kaiser and the Chancellor) bypassed electoral checks and oversights so that innovations like universal male suffrage ended up meaningless. While it was not an absolute monarchy, Wehler asserted that Bismarck was able to use nationalism as a tool to craft an authoritarian state and undermine constitutional checks and balances. Later historians like James Sheehan and Wolfgang Mommsen contended that German structural problems, such as the nation’s vast regional diversity and divergent political and economic developments, contributed to a gradual narrowing of liberalism’s chances to achieve meaningful political success in the united Germany. To many of these historians, the failure of the 1848 Revolutions represented a turning point that failed to turn in that it was a chance to cement national sovereignty inside a parliament. This failure contributed to an aberrant path within Germany's political development (called by historians the Sonderweg).

Around the 1980s, newer generations of historians began to question the determinism and pessimism of Bielefelders and other historians. One of the landmark books questioning the Sonderweg''s teleological aspects was Blackbourn and Eley's The Peculiarities of German History: Bourgeois Society and Politics in Nineteenth-Century Germany. What this book did is examine many of the assumptions of earlier historians and the veracity of their claims of German illiberalism. One aspect that Eley and Blackbourn dissect is using "the West" especially Great Britain as a paradigmatic model for Imperial Germany's lack of democratic development. They contended that such comparisons drew upon a simplified picture of British politics and ignored areas in which German democratic institutions were stronger than the British case. Margaret Lavinia Anderson's Practicing Democracy: Elections and Political Culture in Imperial Germany extended this critique further than Blackbourn and Eley. Her central thesis is that despite Bismarck's antidemocratic intentions, the more Germans participated in democratic elections, the better they got at them. She turns some of the comparisons of Germany with the West on their head by arguing that Imperial Germany lacked such things like "Rotten Burroughs," (safe electoral districts), voter restrictions, and voter patronage systems that were endemic within the allegedly paradigmatic Britain and Western democracies. Anderson argues that the archaic monarchical order was not strong enough to prevent German from experiencing mass democracy, but hindered development enough that “hot family feuds” of the German national community erupted in repressive measures such as the Kulturkampf or the anti-socialist legislation.

The challenges raised by Anderson and other recent scholars like Dieter Langewiesche have not gone unanswered by those historians who see Imperial Germany as fundamentally undemocratic. Volker Berghahn challenged Anderson in an essay in Central European History accusing her of focusing too much on minutia and losing the larger picture of the political trajectory of modern Germany, which eventually led to the Third Reich.

So this leaves the question of "how democratic was Imperial Germany?" open. Part of the crux of the matter depends upon how one defines "democratic". For example, if one defines democracy and citizenship as for the benefit of all citizens irrespective of gender, then Imperial Germany fails along with every other major Western democracy (save New Zealand and Australia) because women's suffrage was not present. Both historiographic camps had differing interpretations of democracy and that colored both of their comparisons with other democracies and their conclusions.

(I'm currently reading "The War That Ended Peace" by Margaret MacMillan, so all this information comes from there.)

Germany was a constitutional monarchy on paper. It wasn't a solid empire as most today understand the word, but a federation of different German states/kingdoms (Bavaria, Baden, Hamburg, Prussia, etc.) with the Kaiser (the King of Prussia) as first among equals. Each constituent state had a representative on a council that (on paper) controlled important matters of state like foreign policy. The Reichstag was the national legislature, elected through universal male suffrage, with the power to pass legislation and approve budgets.

That was all on paper. In reality, Prussia constituted something like 60-ish percent of Germany's territory and population. Because of this, neither the King of Prussia (the Kaiser) nor Bismarck really wanted to share power with the other states. Prussia was also dominated by the conservative Juncker class and so, then, was Germany. The council of representatives from each of the states was pretty much ignored. The Chancellor and ministers were personally appointed and dismissed at the pleasure of the Kaiser.

The Kaiser himself, Wilhelm II, proudly claimed to have never read the German constitution. His vision of the monarch's position in government was much more than being a figurehead giving out medals and rubber-stamping royal assent. He hated having to answer to the Reichstag for anything and insisted that ministers report to him directly. The fact that he had complete discretion to appoint the Chancellor meant that the Kaiser often had more impact on the governing of Germany than the elected Reichstag.

So tl;dr: Germany wasn't technically an absolute monarchy, as there was a constitution limiting the Kaiser's powers, but the Kaiser was still extremely powerful and influential in the government, too much so in my opinion for Imperial Germany to be called a democracy. Elections were free (except for women) and fair, but the Reichstag wasn't nearly as powerful as the UK's Parliament.