Wow.. now that's food for thought and I'm going to take a stab it it.
This child will be born to be a monarch. If for any reason there is a handicap (be it autism, ADHD, physical disability whatever) I think it wouldn't be swept under the rug but given the best there is to assist that child to grow into the fullest capacity the kid can go. Great grandpa Bertie was a stutter and for the most part it was in the background as no one expected him to ever become King.
Should the child be born with any kind of a challenging disability, not only would Will and Kate do the best they can to love, cherish and provide the best there is for whatever condition that child has, it would be something that all children and families with the same challenges would benefit from. Let's say Baby C is born with Down's Syndrome. It would quickly become a national thing for Will and Kate to be involved with. Not just because they have a child affected, but they are going through what a lot of parents of children with Down's Syndrome are.
The days of believing that just because a person has a disability and isn't a "whole" person are in the past and trust me... not a nightmare.
Monarchy wise? I would think the child has a good 18 years for Parliament to declare the "fit for rule" angle. Of course this would be a situation that once again in unprecedented. It'd have to be a wait and see kind of thing.
Speaking of Down's Syndrome again, two specific cases comes to my mind. One is an actor that's absolutely great. Chris Burke. VERY impressive resume I might add.
http://en.wikipedia.org/wiki/Chris_Burke_(actor). The second is a film (the books is better) "A Smile As Big As The Moon".
A Smile as Big as the Moon - Wikipedia, the free encyclopedia
And if it was up to me... should the occasion arise, I'd appoint our own Daria as primary teacher.