Hard to say as the Allies were aware of it but couldn't really stop it till they conquered Germany. Hard to think of what the Allies would have done if there wasn't a war. Good possibility that the Allies would have sat on the sidelines wondering what they should or could do. I would like to think that they would declared war and stopped it but I'm not really sure they would have.
If the Nazis hadn't tried to conquer the world, would other people have attempted to stop their Holocaust? Or would it have been ignored like other genocides?
Given that the USA was engaged in eugenics programs of it's own at the time ... I'm betting Kaywinnet is right. If there hadn't been a war, the rest of the world wouldn't have cared enough to get involved.
In fact, things may have gotten worse ... As the eugenics programs in the USA (and other nations) continued. It's like finding the concentration camps in German territory shocked people to say: "Wow, that's where we're heading. We don't want that."
Eugenics are very much alive and in use. Darwin, Tesla, the X-Club all supported eugenics to weedle out the weak. They said pity was not a useful trait in survival of the fittest and advancement of the species.