Trust me when I say this. The Coptic Church is one of the strictest Oriental churches in ecclesiological theology. My own priest is very very traditionalist (Jonathan, you would love to have a discussion on Chalcedon with him; he is borderline untrustworthy of Eastern Orthodox, and I enjoy debating that with him). The Pope would get very very angry if a priest in public did not wear his "imma" (priestly hat). No one is allowed to change the priestly clothing (one priest tried to where the suit with the collar a long time ago, like the Catholics, and it caused outrage). Very strict sacramental theology, as well. It's only recently when they became comfortable enough to open up to the Orthodox, but other than that, baptism is not recognized at all.
If they are a member of the WCC, I can guarantee 100% that if they were forced to accept the WCC as a Church and membership would require to be part of that church, they would not only leave, but make sure they leave a scar in the WCC, and things would go on without any cordiality for a loooong time. And then, I am well aware, at least the Genuine Orthodox Church and the Coptic Church has something to agree with; they will proclaim Ecumenism is a heresy.
Knowing that my Coptic Church is still a strong member of the WCC, what you believe can't be true. It just can't. But trust me, if it is, I personally wouldn't be quiet about it, and I know many who would join me for that matter.