I think it is more fundamental than that. Emergence always disappears when we slice phenomena thinly. A person walking through a doorway is a very continuous phenomenon. We can see their relation to the doorway at each point. There is no abrupt change. But when we stand back and apply the criterion: "is the person through the door (y/n?)" we end up with an answer. When it is yes, we can say that the passage is an emergent effect of the motion. At one moment it wasn't there, and at another it was.
If emergence disappears when you slice it thinly enough, then the phenomenon was not emergent. There are emergent phenomena in mathematics - for example, infinite sets have many emergent properties that arbitrarily large finite sets don't share. As far as we know, consciousness seems to be an emergent phenomenon, when you increase brain size in some way far enough. Turing completeness is usually emergent as well - remove any single element from a Turing complete system and it typiclaly becomes unable to compute the vast majority of functions.
Is there an accepted definition of consciousness? I thought the definition itself is still under debate. If so, calling an undefined, nebulous thing as an emergent behavior is just silly.
