While that is certainly possible, there's no way you can definitively say "always". Hell, even if some don't vote Democrat, there are still odds that many neo-nazis would vote for an independent or a minor party, or just anyone they shared principles with.
Did you know that in 1988, David Duke (a grand wizard in the Klan) ran for president? Not only that, he /first/ tried to seek nomination for the presidency, in 1980 and in 1988, /from the Democratic Party/, not the Republican Party. He even came close in 1988, but he lost the bid, and then switched to the Populist Party.
And there are other parties they might vote for even now, like the Libertarian Party.
