I don't buy it. The rest of the top Nazis weren't all that credible or even coherent at Nuremberg. Goering was barely getting over his drug addiction, and spent most of his time trying to shout down his lawyers and fellow defendants.
Furthermore, the Allies sure as hell aren't going to let the trial turn into some grand opportunity for the Nazis to propagandize. There was enough material to condemn them in the eyes of the world without Hitler puking all over Judge Biddle on film. Even if the Nazis put together a ticker tape parade in the courtroom, they will come out the bad guys.
Hitler puking all over Judge Biddle was the most sad scene in the whole WW2 saga. It show's how bad Hitlers health had become. As for Goering he was just acting for the camera's.