No, Montgomery did get the green light for Market Garden. The drive wasn't toward Berlin, however. It was intended to go from Holland into the Ruhr, cutting off much of the coal and steel, and cutting off the German troops west of the Rhine.
I am not a military historian and do not know the details. It was not market garden tho. The only reason I mentioned it is many years ago, in one of the books on Patton it was mentioned that he saw a weakness and knew if it was taken advantage of he could drive straight to Berlin.
What really piqued my interest was I was recently reading about Montgomery and noticed he had thought the exact same thing. I honestly think both Patton and Montgomery were on to something. It had nothing to do with how many resources the Germans had left but with the fact that a weakness was seen which taken advantage of, they believed would work. It was one of those rare times when Patton and Montgomery agreed.
Of course no one knows what would have actually happened. It reminds me of something I read in a book by Adolph Galland. He said during to attack on Poland, a Polish General saw an opportunity to destroy the German Army and began to do it. The Germans were saved by .88mm anti aircraft artillery being used against troops which they had never been intended for. Galland said the Germans actually came close to losing that war.