I'd say it's a fairly obvious connection, not only to Nazism but to other ideologies of the same crazy variety as well; racial supremacy or nationalist groups for example. Or religious cults.
Although the comparisons to the Third Reich are probably the most prevalent: The inscription at the entrance to Nurmengard, Grindelwald's prison for (political?) enemies, "For the greater good", is eerily similar to the phrase "Arbeit macht frei" (something like: Work will set you free) that was put up at a number of concentration camps, including Auschwitz.
And I definitely think that this was done deliberately by JK - after all, the Harry Potter books are, to a considerable extent, trying to teach tolerance.

In before Godwin's Law.