No, not really. There are far better reasons why Hitler chose that mustache than to resemble some American comedian.
British comedian, actually. Well, British expat comedian in America (but left permanently when McCarthyism kicked in).
Here's a Chaplin-Hitler toothbrush mustache timeline:
-1914 : Chaplin sports a fake toothbrush mustache as "The Tramp." The mustache is used to either "age" the young Chaplin (4 days older than Hitler) and/or to make sure facial expressions (in the silent era) are easily understood.
-Between 1916 and 1923 : Hitler shortens his longer mustache (I've seen one picture of that) into a toothbrush mustache. This is either because of WWI gas-mask restrictions, or for stylistic purposes (it may have been a little popular in Europe at the time), or even, as one poster suggested, to resemble "The Tramp" in some kind of a joking, family friendly way. This only makes sense if it occurred around 1920-1921 when Hitler was beginning his "career" as a Party orator (although his speeches weren't particularly family friendly).
-Early 1930s : Hitler gains notoriety around the world. As does his mustache.
- 1936 : The film "Modern Times" is released, and Chaplin publicly retires his Tramp character and image.
- 1939 : World War II arguably begins.
- 1940 : Chaplin's first movie after retiring "The Tramp" features a Tramp-like character in "The Great Dictator." The film is made, supposedly, because of Hitler's and "The Tramp's" similar look, although the character does not appear. Chaplin, an agnostic who does not refute the erroneous comments that he might be Jewish, parodies Hitler and makes fun of his antisemitism, etc.
-1941 : Germany declares war on America