Of course. It’s satire, and it’s brilliant.
Werner Klemperer, whose family fled the Nazis, said he would take the role of Klink only if the character would never be allowed to succeed.
Interesting story about Robert Clary, who played LeBeau and was a concentration camp survivor: in the 1966 episode “Will The Real Adolf Please Stand Up”, Larry Hovis’ character of Carter impersonates Hitler (and rather well). As Carter/Hitler is introduced to the prisoners, he is given a Nazi salute. Clary’s salute is given with his left hand and with his fingers crossed.
Mr. Klemperer was absolutely brilliant in his role as Emil Hahn, a bitter and utterly unrepentant Nazi, in Judgment at Nuremberg.

Drifting completely off-topic, but triggered by the Klemperer surname, permit me to recommend a duo of books by Victor Klemperer. They are actually his diaries during the rise of the National Socialists (emphasis on the letter intentional) in Germany. The Amazon synopsis of I Will Bear Witness: A Diary of the Nazi Years, 1933-1941 doesn't begin to adequately describe these most enduring volumes:
The publication of Victor Klemperer's secret diaries brings to light one of the most extraordinary documents of the Nazi period. "In its cool, lucid style and power of observation," said The New York Times, "it is the best written, most evocative, most observant record of daily life in the Third Reich." I Will Bear Witness is a work of literature as well as a revelation of the day-by-day horror of the Nazi years. A Dresden Jew, a veteran of World War I, a man of letters and historian of great sophistication, Klemperer recognized the danger of Hitler as early as 1933. His diaries, written in secrecy, provide a vivid account of everyday life in Hitler's Germany.