From my limited personal experience of Home edded children joining school during primary (just 3 children), they were a delight and challenge to accepted school norms.
Two used to answer (essentially rhetorical) questions asked in assembly, or put in a comment or question about what the speaker said. So refreshing when everyone else (teachers included, often) tended just to sit there blankly.
All three used to ask 'why?' regularly in class when asked to do something. That is a really good question to ask a teacher, and an even better question for the teacher to ask themselves! There should be a goood answer to the question, and they were usually happy to do the activity once the explanation was made. Sometimes it led to a change in activity or more choice for the whole class too.
Sadly, in many ways, the children became institutionalized very quickly, and would have been largely unspottable from the rest after a term or so. I mean institutionalsed in the nicest possible way. They remained engaged, confident, enthusiastic learners, but they stopped speaking out when something just occurred to them, and went along with the group routines and activities.
Incidentally - and this is absolutely not a representative sample, obviously - all three had noticably uneven academic profiles, reflecting their, and I assume their parents', interests or strengths. They each needed extra help in some areas (eg. aspects of maths, problem solving, geography, PE, science) but were well on in others (eg. reading, arithmetic, music, art).