Listened to this one for a second time, and I settled somewhere in between Ryan (and half Teague) and The Rest. I differentiate between acting performance, animation, and visual effects, but think that all three can be involved in various amounts to produce a character. The involvement of more than one does not negate the eligibility of the others, in my mind, though the extent to which each is involved can effect whether there is enough of another's involvement to be nominated.
I especially differentiate between acting performance and animation, where performance is done in a somewhat real time environment, where animation is not real time and can be revised. I see them as different and distinct arts. I would also argue that on-set puppetry is closer to acting performance than animation, hence inclusion with SAG. CG puppetry goes with animation.
In cases where an actor provided performance, animators changed the performance, and visual effects artists added the 'make up', the question to me is not whether they're each eligible, but whether their work had enough impact on the final product to warrant nomination. I suppose this could lead to bake-off situations for the acting performance categories, but to take Bryan's screenplay vs. ad-lib example, I suspect you have to show that your screenplay effectively made it to the screen. It's not that strange an idea.
While I'm sure there are cases where the resulting character is 50/50 actor performance and animator animation, I can't see the result getting nominated in both categories, as I doubt there would be enough of either to make the Oscars happy (where best usually = most). If the same person did the performance and the animation then they just covered two arts.
Examples!
Caesar - I would say that there was a lot of performance, very little animation, and a lot of visual effects. Serkis is eligible for performance nomination, the animators for animating, and the visual effects people for the visual effects. I'm not saying that any of those groups deserve nomination, just that they could be if they contributed enough to the result. In this case, the animators would probably not be nomiatable due to their comparatively minor contribution. As far as I'm concerned, whether or not Serkis was involved in the post-production of Caesar is irrelevant to his performance, which was complete when the cameras stopped rolling.
Elephant man - Same deal, with actor providing performance and make-up the 'visual effects'. I don't differentiate between post-production or pre-production visual effects/make-up. I could see a future where algorithms are pre-programmed to add the pixels to an actor's performance on the fly, just like make-up. Whether it was done before or after is irrelevant to me.
Teague's hypothetical crappy actor saved by animators - I could see the animators dragging out before and after and saying 'see, we totally did this and we're awesome'. Pixar would often brag that they had no motion capture involved in their animation. The actor could still be 'eligible' as he did do a performance, but nomination would be unlikely just like an actor cut out of a movie in editing.
Rango - Actors still eligible, as long as they can demonstrate that the actors' performance contributed significantly to the resulting characters.
Totally animated character with voice actor - Movies being a largely visual medium, I think you need some visual aspect to the acting performance to qualify as 'enough performance' for likely nomination. I'm not saying that voice acting isn't a performance, just that it might not be enough (best=most).
Awesome puppet performance - Tricky in cases where multiple people contributed to the performance, but hypothetically possible if they could demonstrate that one person really put the soul into the character on set.
Final note: I suspect there isn't an Oscar for 'best animated character' or even 'best animation' (the art, not the movie genre), which somewhat confuses my argument. I would rather see that category than Teague's suggestion of 'best composite character', and I would definitely rather it to the 'best animated movie' category/ghetto that exists now.