From the Goddess's lines, I would think that Lappi didn't have an existence as a human or anything like that prior to having her soul put in the plushie — that the Goddess created her for that purpose. (Otherwise she'd be released back into samsara to be reincarnated rather than just joining with the Goddess.)
I agree that there are a lot of parallels that can be drawn to disability or to asexuality. Not that it's necessarily a direct allegory, but that the analogy is there to be seen. It's really very sweet.
(And that's kinda why I think it'd be a mistake to have a sequel where Lappi turns into a human. Megu says she still has her magic — but she's already said what that magic is: it's love. It's enough, because it has to be enough.)
What's the word for what was done in creating Lappi, by the way? "Incarnated" implies flesh, as its root is "carne", Latin for meat. Was she inlanated? ("Lana" -> "Wool").