Do you think that Chiyo-chichi really is Chiyo's father? It's pretty interesting. I would think that it's not impossible, since this is set in the same world as Wallaby, where a stuffed animal is possessed by the soul of a dead boy. But I'm seeing two options. One is that Chiyo-chichi is Chiyo's father, but she doesn't know it. When Osaka gives her the plushie shaped like him, she doesn't seem to recognize it, and when Sakaki says that he is Chiyo's father, she only appears confused. But she does have parents; she wakes them up at her house (she has two). But they could be her adoptive parents, and she doesn't know that she's adopted?
The other option is that Chiyo-chichi is simply a figment of Sakaki's imagination. He comes in the shape of a stuffed animal, and Sakaki would probably be hanging out at places where they sell stuffed animals. She could have noticed him subconsciously, and then dreamed about him. But then why did Osaka dream about the cat being Chiyo's father? Probably because she was there when Sakaki said the plushie was Chiyo's dad. She might have remembered that subconsciously, and then it showed up in her dream.
What do you think? There seems to be a brand for Chiyo-chichi in-universe. Especially in Yotsuba where Fuuka has a lot of Chiyo-chichi merch. About Fuuka, either Yotsuba&! is set in the same universe as Azumanga Daioh, or Fuuka is just a fan of Azumanga Daioh. Anyway, Azumanga Daioh and Wallaby are set in the same universe, since Kokoro appears in both.