No, but let's not forget that much of statistics was originally invented to provide a rigorous underpinning for eugenics. Pearson, who invented many of the most commonly used statistical results, was a prominent eugenicist and contributed greatly to its ideas.

That doesn't mean that statistics aren't a useful tool for checking the strength of evidence, or building a case for a hypothesis.

Sure, but it doesn't change the fact that your findings will be as useful or useless as your premise. If you're trying to use statsitics to prove pseudoscience, well, it's still pseudoscience at the end of the day. (NB: I don't mean that psychological sciences are pseudoscience.)