Speaking from my own big tech hiring experience, as the hiring manager, and working with our recruiters from HR, if you do not belong to one of the "in demand" demographics, then it generally does not make a difference between providing the true value and declining to provide that information, because the positive identification of underrepresented groups was the part that made a difference.

I never got to see the responses myself, but the recruiters from HR could. That said, if a hiring manager wants to bias their hiring based on this information, they'll figure out at some point before making a decision, whether or not you provided it. Your resume, your name, your educational background, your accent, etc. all passively shed information, so I would often find the answers without wanting to or trying to find them.