Actually, you can absolutely use social science methods to attempt to demonstrate (or in this case, disprove) these kinds of links. But let's put that aside for a moment, and discuss what is objectionable about the memo.
What are the costs/benefits of having this "debate" at work over a hypothesis that cannot be proven, as you state?
Look again at what the author was doing. He was using scientifically demonstrated biological and psychological differences between men and women (women have "higher agreeableness") to hypothesize about how that affects their work choices and, notably, their performance ("This leads to women generally having a harder time ... speaking up, and leading.").
What this is doing is connecting a gender stereotype (which, sure, is scientifically supported in aggregate - that's true for a lot of stereotypes!) to work practices and outcomes. The authors claimed benefits of presuming that this connection is true are basically a) this will make conservatives feel more accepted at work, and b) diversity is "bad for business" (which is just provably wrong by an enormous amount of evidence that the author ignores). I think a) is absolutely a worthy benefit, but there are lots of other ways to do this without linking gender stereotypes to work performance!
Now let's look at the harms of having this "debate", particularly at work, which are numerous and measurable. While there are no studies demonstrating the link between biology and STEM job performance, there are many studies demonstrating the impact of widespread gender bias in STEM fields (classic recent reference: http://www.pnas.org/content/109/41/16474.abstract) and how it affects hiring and advancement. The memo's author correctly acknowledges these types of biases. So the harm is perpetuating gender biases in the workplace that affects people's careers. Not to mention the harms of opening up Google to gender discrimination lawsuits (ala https://en.wikipedia.org/wiki/Price_Waterhouse_v._Hopkins), the productivity cost of employees who don't want to work with people with publicly broadcasted unproven gender biases that could affect their decision making ("hostile work environment"), etc. And not to mention losing the many economic benefits that a company reaps with a diverse, inclusive workplace.
So no, I don't think it's worth having this "debate", especially at work, where the benefits are negligible at best, and the harms are clear. If you want to have this debate, go write a medium article or something. Don't send this around your workplace. It's not that hard, really. People call this thought policing, or groupthink or whatever, but it's just harmful and a waste of time at work.