The German Empire in 1871 was nearly 2 1/2 times as large (in area) as Prussia alone had been 11 years earlier:
According to Wikipedia the population of Prussia in 1871 was 24.6MM, and that of the entire German Empire was 40.0MM; note of course that the former includes all the territories conquered/coalesced in the preceding decade.
The German Empire's vast reserves of coal and iron ore in the Rhineland as well as Silesia helped it to achieve a significant increase in urbanization in the years following 1861, rapidly increasing urbanization from 30% of population to over 65% in just 20 years. (I had that reference a moment ago and lost it - sigh.)
All these factors combined to drive a significant increase in national wealth from Prussia alone in 1861, to the entire German Empire in 1881.
So, to answer your question, the German Empire did not drive the economic and scientific success of the German population, but it did mean that a single autocratic government subsequently wielded the influence resulting from that success.
Note the German Empire generally (as well as Prussia specifically) entered the Industrial Revolution somewhat later than Britain, despite having significant geographic resources beneficial to that process. It is entirely expected that as the Industrial Revolution slowed in Britain the later starters would catch up.