This cartoon was included in one of the Warner Brothers Golden Collections of cartoons - it even included a commentary. All during the commentary the two doing the commenting only talk about the fast pace and how Daffy's personality seems so much like that of one of the animators over at Termite Terrace - which is where the WB cartoons of the era were created. Nobody mentions the 500 pound gorilla in the room - which is that Daffy in this cartoon is virtually alone in any film or cartoon I have viewed from the WWII era in that he is afraid of being drafted and stays afraid. Plus Daffy is willing to do anything - including doing severe bodily injury to the man from the draft board - to avoid being drafted.
I wonder how this went over with the audiences of the era? Maybe Daffy Duck got away with this because Daffy usually represented unbridled greed, cowardice, and self-interest to the point of being charming - he never made excuses for himself. Likewise "the little man from the draft board" looks a great deal like Elmer Fudd, so it's really hard to take him seriously too. Definitely worth a look if it crosses your path.