Catagory 2 men

Eugene Volokh points out an interesting distinction about social interactions. I, like him, fit into catagory two. My main question (and it's a self-serving one) is different from his. Do catagory two men and catagory three women in general have a more difficult time initiating romantic relationships? Intuitively, it makes sense that they would, because the line between somebody who is a potential mate and somebody who is a potential friend is much blurrier. I suppose the same would go for homosexual type one men and type four women. I guess that my real question is does it work out empirically as well as intuitively?