Of course men and women can have platonic relationships. The archaic and antiquated thinking perpetuated by media and mass marketing continue to stereotype and separate genders and cause confusion. Platonic relationships have a much better chance of survival than romantic ones and offer a better and more in-depth degree of understanding. Not only is a platonic relationship possible, it's probable.
Yes I think that it is possible for a man and a woman to have a platonic relationship. Some women get along better with men as friends. Some men get along better with women as friends. A lot of times these relationships do not harbor romantic feeling for one another.