If you're asking, was Nazism affected by these theories and did it embrace them as state ideology, the answer here is clearly yes and very explicitly so. Nazi ideology was explicitly eugenic and explicitly couched its policies and approaches to race in the language of scientific racism. It was not an incidental part of the ideology — the racial approach was core to it, and is reflected in not only what they said (e.g., the propaganda) but what they did (their laws, educational and medical policies, and their violence).

But if you're asking about causality, e.g., did the theories lead to Nazism, that's a very different and difficult kind of historical question to answer. I would not say that Nazism "grew out" of scientific theories. It had its own historical antecedents, which included said theories as part of that context, but was not exclusively said theories. Nazism grew out of class conflicts within Germany, it grew out of the context of the end of World War I, it grew out of strife with Communism, and many other factors. And the appeal of said theories was not their scientific merit, of course, but the way in which they reinforced the racist beliefs that these other contexts also reinforced. (I do not go as far as some who basically say that "scientific racism" is just an appealing front for "vulgar racism" — I think the interaction between the two is probably more complicated than that — but I also don't go as far as thinking that the "scientific theories" are pushing things along by themselves. There is a complicated feedback loop going on in these kinds of situations.)

Scientific theories on race, as well as eugenic arguments, and the concept of Rassenhygiene (racial hygiene) were definitely a key part of the "mix" that made up Nazism, and were core to Nazism (in a way that they were not for Italian Fascism, by contrast). But anything as complex as a mass political movement or ideology is going to have a complicated relationship with the many factors that motivate it.

The best book on the role of these theories within Nazism and the Nazi state is Proctor's Racial Hygiene.