I do not believe so. You have to remember that Paul is speaking of those who believe and accept Christ. Christ does not reign and is not the head of a man that does not receive Him. But every man could receive Him and if that man were to receive Him, Christ would be the head of every man, and when he was speaking of man in this verse, he was referring to gender. I will show the verses.
"...I am not seeking my own good but the good of many, so that they may be saved. Follow my example, as I follow the example of Christ. I praise you for remembering me in everything and for holding to the traditions just as I passed them on to you. But I want you to realize that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God."
Paul is speaking primarily to believers, but also to those who might come to the knowledge that leads to salvation. And of course, this is not a very popular verse among women, so I don't blame you for not quoting it in its entirety, but Paul doesn't seem to have been referring to mankind in that verse, but the men who are in Christ, and those who might come to be in Christ.