My answer: No.
Let's take a look at a quote from the movie When Harry Met Sally, which centers on this question.
Harry: Yes, that's right, they can't be friends. Unless both of them are involved with other people, then they can... This is an amendment to the earlier rule. If the two people are in relationships, the pressure of possible involvement is lifted... That doesn't work either, because what happens then is, the person you're involved with can't understand why you need to be friends with the person you're just friends with. Like it means something is missing from the relationship and why do you have to go outside to get it? And when you say "No, no, no it's not true, nothing is missing from the relationship," the person you're involved with then accuses you of being secretly attracted to the person you're just friends with, which you probably are. I mean, come on, who the hell are we kidding, let's face it. Which brings us back to the earlier rule before the amendment, which is men and women can't be friends.
Okay, first of all, why don't we define "friendship." I think here, "friendship" means not just someone you talk to in class or at work or casually whenever you happen to run into them. I think here friendship includes going out of your way to make plans with this person, like lunch, coffee, or a movie. And here, friendship also includes mutual sharing of things you wouldn't ordinarily share with just anyone that you know.
I think that men and women cannot really be friends (using the above definition of friendship) without either or both of them having feelings for the other at some point in the relationship. This isn't to say that two friends can't move past these feelings to have a completely platonic, yet still intimate friendship. Because that has happened to me. But if you're going to become emotionally intimate with a person of the opposite sex, one or both of you will start to have feelings for the other.
And this presents an enormous problem when one the two friends are involved with other people, as the above quote examines. When a person is in a committed romantic relationship with another person, I think there is something wrong with the relationship when one or both of those people seek outside companionship from another person of the opposite sex.
So, short answer: No. There you go. I might add more to this post later, if I feel I wasn't explanatory enough.