Let me start with the last first. Of course it wouldn't have. If there were other social forces tending toward it, then no well-meaning legislation could have prevented that.
On the other hand, if you look at Europe in the 1930s, there is a very good case to be made that the consistent and incessant demonization of the Jewish people led to a moral anesthesia among the population of a number of countries that allowed otherwise intelligent westernized people to stand by and to look aside as the most horrid acts were perpetrated by a very resolute racist regime.