I had the same concerns when I was thinking about sending in my Sam (who was badly in need of a new head!). She had very thin hair left, probably because I took her everywhere with me when I was little. She was my best friend. I was totally afraid that if I got a new head on her, she wouldn't be the same.
Right before my Sam turned 15 years old, I took the plunge and I got a new head for her and I was so excited to see her come back and even more excited that she was still my same Sam (just with more hair to play with). Now I'm considering sending in my Lissie (who will be 15 years old Christmas 2006). Your Sadie will be the same when she comes back. They do a great job!