It wasn't like that. She did want to do some role in the show, I remember her saying that she was willing to do anything, even a little walk in part, she just wanted to be in the show. Dawn was really meant to be in the show and the thing that Michelle wanted to be part of the show had nothing to do with it...
They were looking for someone to play the part of Dawn when Michelle came to see Sarah in the set (they've known each other years before Buffy) and Sarah talked to Joss that maybe Michelle could do the role. Michelle did screen test and was casted. Actually they were looking someone younger to play the part 'cause Dawn was meant to be couple years younger but because Michelle was perfect for the role they give it to her and made Dawn little bit older. That's what they say in s5 dvd box (uk version) set's interview if I remember correctly... 🙂