I don't think so. You'd have to be upper-middle class to upper class to go and Hermione has always struck me as pretty middle- middle class. I've never heard of someone going to the same boarding school as their parents - I think that was the norm in the first half of the 20th century but isn't any more. I think chances are Hermionie would have gone to the local private school (I'm not sure where she lives) but if the local one wasn't very good she may have gone to boarding school, as they do tend to be very, very academic. Hope that helps.