Yes, it is possible for a man and a woman to have a platonic relationship. Not all relationships between the two sexes are based on attraction. This question is also a bit insulting to homosexuals, who never have an attraction of any sort to the opposite sex. Therefore, men and women can have platonic relationships.
Whether you subscribe to the theory of evolution or creationism, the need to procreate is much greater than any type of label a man and woman can use to characterize their relationship. All relationships between men and women have an under current that is sexual in nature. And, in the right circumstances, human nature does and will take over, if the couple continues to spend enough time together in the right circumstances. Ultimately, their relationship will move from platonic to sexual.