The short answer is no. But the real world answer, I believe, is more complicated.
We have no legal responsibility to extend Constitutional rights, or even the Geneva Convention to the detainees at Gitmo. It is by no means cruel or unusual to deny them the rights of a system they detest as much as ours.
But that's not the point.
The point is, we are waging a war that's as much about perception as anything. Like it or not, long term success (translated: success AFTER our troops have returned home) depends greatly on the respect that the Iraqis and others in the Middle East have of our judicial system and our stance on human rights. While I personally believe the media has overstated the situation at Gitmo, I do think that we have "pushed the envelope". The fact that they're being held anonymously, and without being charged, says as much.
I believe in the superiority of the US Constitution, when its rights and duties are respected. It is a document that provides for greater potential liberty than virtually any other constitution in history, and certainly greater liberties than any constitution in existence.
And so, we would do well to prove it. Give the Gitmo detainees due process, give them a fair trial. Give them the rights that they would have if they were American citizens. After all, that is what they are (ironically) demanding. Let's show the rest of the world that our system is INDEED superior and that the evil deeds of the terrorists were exactly that.
But that's a point we can't prove if we keep them locked up in anonymity.
But that's just my two cents.