Star Piece does increase dust rewards from quests.

Just evolved my Gyarados and claimed rewards. Just before the evolution, I popped a star piece and lucky egg. While the win screen told me I got +3000 dust for completing that phase of the quest, I wrote down my dust totals before and after, and the difference was 4500. So it does give you the bonus dust for the star piece, but doesn't tell you that it does. Just want to get this out there so people know about it. And when I finish the last stage, I certainly plan to have both going again.