I have no stakes in this, but I think he will be the starting QB. The reason he isn't usually the backup during game weeks is because they give him snaps all over the offense in preparation for games. And they have the luxury of carrying 3 QB's and can rely on Winston if either Brees or Hill gets hurt during a game. But now with Brees out they have to rely on Hill. They can't use Hill in the same role with Winston starting with their only other backup being Siemian who they just signed.
So, I see them rolling out Hill as the starting QB and backing him up with Winston in the role Winston has had all season. I think we will see less of the unique Hill plays this week, but I could be way off.