If Sylar were to somehow actually get Claire and cut her brain out and eat it (that is what he does, isn't it? i missed a couple episodes), would Claire be able to regrow her brain and fix her skull, so she's still alive, and Sylar has her powers? Is her healing factor powerful enough for that?
He doesn't eat brains, he simply looks at them.
Sylar's ability is the ability to see how things work just by looking at it.
The way I understand it is this:
We all use approx. 10% of our brains. So there is 90% of our brainpower not being used. I think this show suggests that within that 90% of unused brainpower is the ability to do all these things, these 'powers', that we see the characters doing on the show.
If a person were to have control over 100% of their brain, they'd be able to do EVERYTHING you see on this show: flying, healing, telekenisis, pyrokenesis, invisibility, etc. Everyone carries all these dormant abilities, it's just that most people don't 'access' to that part of their brain.
Now for one reason or another, some people have 'access' to a part of their brain that not everyone else does. For example, I can flair my nostrils. Some people can't. How do I explain to someone who doesn't know how to flair their nostrils? I can't. I just happen to know how to do it. Some people can wiggle their ears. I can't. And nobody will ever be able to tell me how to, cause I don't have the part of my brain that knows how to do so 'unlocked'.
So the same could be said about these other much more interesting abilities. Claire knows how to heal herself because she just happens to have that specific part of her brain accessed. Matt can hear people's thoughts because he just knows how to. Etc, Etc. Nobody can explain to another person how to do the same. You can either do it, or you can't.
Still with me? Good.
Now enter Sylar. With his ability of knowing how things work simply by looking at it, he's learned that by simply looking at the brain of someone, he can 'learn' how a person's brain can be used to use a specific ability. For example, by looking at the brain of the guy who could use telekenisis, he could see how his brain needs to work in order for him to do the same thing. I imagine that if he looked at my brain he could 'learn' how to flair his nostrils, something I could never explain to him how to do in words.
I hope that makes sense. That's how I see it anyway. Perhaps I'm wrong, but it makes complete sense to me.
So yeah, Sylar doesn't eat brains as we first thought...he simply looks at them so he can learn to do what they could do.
And as for the topic question, I'm not completely sure. On one hand we saw Claire actually die when she got that branch jabbed into her brain, so I'd think that as long as there's something actively damaging her brain (the key to being able to use her ability), then she can't heal. BUT, as soon as that branch was pulled, her brain DID heal, along with the rest of her.
So if someone who DOES eat brains (like Venom?
) were to eat her brain, could she regrow one? Hmm...I'm not sure. If her brain is removed completely, then there's no brain left in her body to say "heal".
But interestingly enough, I think that a person DID eat her brain, then her brain itself would be able to regrow a whole new body, possibly even while inside Venom's body!
So I suppose my final answer/assumption is this:
Can Claire's body grow back a new brain? - No.
Can Claire's brain grow back a new body? - Yes.