I empathise, we have an unmotivated son as well. We have always felt that he would do the absolute bare minimum no matter what school he went to, but hoped that at CH the bare minimum would at least be quite a high standard. It's fair to say that our son has not exceeded our expectations so far, and we will find out this summer what that translates to in GCSE terms.
Rest assured, the school will not "cast him adrift". They will do what they can and they won't give up on him.
However, there are some aspects of the education process that the school could do better. There are some pretty uninspiring teachers there (in the science department there are a LOT of uninspiring teachers there) who do nothing to bring their subject to life. CH gets very strong results in science, but I don't think their success is due to the quality of the science teaching. If you think your son might want to pursue a science-oriented career I would recommend that you think about sending him somewhere else where the teachers might be better equipped to find some spark of enthusiasm within him.
I have heard similar stories from a disillusioned mother of a boy at CH. She says that many of the boys are tutored at home (often with 2 or 3 tutors) and parents have to go over the day's lessons and teach what the teachers have left out!