Did the eugenics program in Nazi Germany have a measurable effect?
As most of the comment have pointed it out, It's nearly impossible to find out. This is my try:

Dr. L Alexander wrote in his paper, Medical Science under Dictatorship:


  Hitler issued the first direct order for euthanasia in Germany on
  September 1, 1939, as his Panzers moved on the Blitzkrieg of Poland.
  Organizations with humanitarian-sounding names were immediately set up
  to execute "health" programs, again, under deceptively, euphemistic
  terms. For example, questionnaires collected by a "Realm's Work
  Committee of Institutions for Cure and Care" gathered and reported
  information on patients who had been ill five years or more and who
  were unable to work. "On the basis of name, race, marital status,
  nationality, next of kin, whether regularly visited and by whom, who
  bore financial responsibility, and so forth," decisions were made at
  key universities about which patients should be killed by
  psychiatrists who had themselves never seen the patients.Likewise, the
  "Realm's Committee for Scientific Approach to Severe Illness Due to Heredity and Constitution" was exclusively devoted to the killing of
  children with congenital anomalies or chronic illnesses. In all,
  275,000 people were put to death in these killing centers before the
  Nazi Holocaust. 




Law for the Prevention of Offspring with Hereditary Diseases (July 14, 1933)


  Anyone suffering from a hereditary disease can be sterilized by a
  surgical operation if, according to the experience of medical science,
  there is a high probability that his offspring will suffer from
  serious physical or mental defects of a hereditary nature.    Anyone
  suffering from any of the following diseases is considered
  hereditarily diseased   under this law: 
  
  1. Congenital mental deficiency, 
  
  2. Schizophrenia, 
  
  3. Manic-depression, 
  
  4. Hereditary epilepsy, 
  
  5. Hereditary St. Vitus’ Dance (Huntington’s Chorea), 
  
  6. Hereditary blindness, 
  
  7. Hereditary deafness, 
  
  8. Serious hereditary physical deformity. 
  
  Furthermore, anyone suffering from chronic alcoholism can be sterilized.


If anyone is trying to get the statistical evidence that Eugenics have even remotely successful, have look at this table:

 

Current Top 50 death causes of Germany. (Rate = $\frac{death}{1000}$)



They have started various ways to brainwash people, one of them was movies.

$\text{Ich klage an}$


(source: filmportal.de)  

Plot: A woman suffering from multiple sclerosis pleads with doctors to kill her

Current Scenario: Germany Rank $18^{th}$ in the world in death due to Multiple sclerosis

Source:


Alexander L. Medical science under dictatorship. N Engl J Med 1949;July 14. 
http://www.life.org.nz/euthanasia/abouteuthanasia/history-euthanasia6
Table: WHO, World Bank, UNESCO, CIA and individual country databases for global health and causes of death.