It certainly would, and you can observe it doing so. Our understanding of one another cannot be complete. There can be no true communal standard as to what 'rabbit' actually means, and as we move away from the central anchor of 'rabbit-hood' we will disagree on what features things need to retain in order to remain 'rabbits'.
This variation is sterner and broader in children than adults. Notoriously, way too many things are doggies for a while, and kids disagree a whole lot more on what doggy-hood is depending on whether they have contrasting notions of kitty-hood or horsey-hood mixed into their experience. They make those guesses and fight with one another about them, or test them by how adults respond to their usage. Language is a game more like 'tea time' than like 'Monopoly', we learn what the rules are by taking part, not by being told.
Humans don't learn definitions or grammar as children, because we know that is impossible, basically from logic like Quine's (more specifically, but less clearly, Wittgenstein's). Instead, we converge on vague complexes of meaning and usage until we have enough structure to conceive of the notion of a definition and its surrounding grammar. Then we change the way we talk about words, because that structure is a lot more efficient, even if it is less than honest.
This is part of the motivation for Chomsky presuming children have a native ability to vet guesses about meaning against pre-established patterns of grammar. It seemed insurmountable to him that children could both deal with vagueness and learn grammar at the same time, without some built-in instinct for what parts of language were which sort of thing. But apparently we do.