What would Carson's argument be? I think it's clear from context. Incentives work. Incentives affect behavior. Once the word got out that Jews were being hauled off to death camps, the Germans doing the hauling would have had to think twice before going after Jews in their homes if they had known that Jews were armed. But Hitler's gun control law of 1938, along with earlier gun control dating from 1928, left most Jews unarmed. Legal scholar Stephen P. Holbrook has written about this at length. In "Nazi Firearms Law and the Disarming of the German Jews," he tells about Hitler's systematic, and unfortunately successful, efforts to disarm German Jews.
Ben Carson has a right to his views on gun control, but the notion that Hitler's gun-control policy contributed to the Holocaust is historically inaccurate. The small number of personal firearms available to Germany's Jews in 1938 could in no way have stopped the totalitarian power of the Nazi German state.
Notice two things about that statement:
1. In the last part, the ADL changes the subject. Carson was not claiming that had Jews been more armed they would "have stopped the totalitarian power of the Nazi German state." That's a tall order. He was, instead, saying "The likelihood of Hitler being able to accomplish his goals would have been greatly diminished if the people had been armed." I took that to mean that Hitler would have had a tougher time achieving this particular goal--murdering German Jews--not that, had Jews been more armed, he would not have used the totalitarian state for many of the other evils he committed.
2. It's not even clear that the ADL disagrees. Read the second sentence above again:
The small number of personal firearms available to Germany's Jews in 1938 could in no way have stopped the totalitarian power of the Nazi German state.
Notice its emphasis on "the small number of personal firearms" owned by Germany's Jews. The ADL seems to think that the number of firearms matters. Fewer firearms: less resistance. More firearms: more resistance. That's what Carson is saying. And one main cause of lack of firearms was Hitler's gun control.
UPDATE: Friends who know the issue better me agree that incentives matter but that they wouldn't have mattered much. So I won't defend Carson's statement. I will defend this statement (of mine): "Some of the Jews who were murdered by Hitler would not have been murdered if not for Germany's control laws. I am confident that the number saved would have been more than zero but probably would have been less than 10,000. But, hey, if 1,000 lives had been saved, that would have been a good thing. They've made movies about such numbers."