He gambled that Britain and France would back down over it just like they did with czechoslovakia. They did not.
Poland was not going to give Germany back the "Polish Corridor" through any other means than Germany taking it from them.
Hitler gambled that war would not start until 1945, So yes it really could of changed many things. For instance if the Allies did Nothing Germany would be even stronger than in 1940, but then so would the Allies.