I don't think this falls under the 'logical' range. Packers/Bears is one of the oldest rivalries in the NFL. Given the opportunity to knock the Bears out of the playoffs, I think we'd start our A team and keep them in the game if it were close.
The only way I'd see us resting the starters (especially if we had a bye the next week) would be if we were getting blown out, or blowing them out.
I wouldn't expect the Bears to do any different than we would. So, IMO, if we want their starters out of the game we need to thump them hard right from the start of the game. 'Cause we don't want them pulling them because they're blowing US out... 😞