Probably not. As a freshman in college I tried to provide all the "right" answers on one of those kinds of personality tests and failed. I then did research and produced a term paper for an introductory psychology course on how my scores made me appear a little too much on the nutty side and explored the reasons why. The answer I posited was my high creativity level, which I backed up with evidence from other kinds of tests. I received an "A."
That was in college. In the real world the wrong kinds of scores on personality tests could mean not getting a job. There's where the issue could become a legal one, reports THE WALL STREET JOURNAL. Those who somehow find out that they had been knocked out of the box by the scores are now taking their beef to the U.S. EEOC.
The trick, though, is being able to prove that it was the scoring on the test which resulted in not getting a job. With so many variables going into a hiring decision, that's not easy. It will become a lot harder now that employers are wised up that the EEOC is monitoring the situation.
In my 20s, I took a series of tests to become a something or other at Merrill Lynch. I was not hired. Later there was a class action law suit I was invited to join against Merrill Lynch for discriminating against women and people of color. I didn't. That memory of scoring a little nutty back in college still haunted me and I assumed that I had just come across badly aka not businesslike in the tests. Incidentally, in my late 40s, I took a similar series of tests at American Express. They told me that I had not fit the profile but based on other criteria they did allow me into the financial planner training program.