The way he fell off two seasons ago, I'd be awfully surprised if that happened. If it did, I expect it would after the start of the regular season, when they could sign him and not guarantee his salary for the year. When does that happen, after the week 1 game or is it just before?
I know it's the Bears and anything can happen, but I can't see being too concerned about week 1. That team is a disaster. I think they play week 1 with what they have, and make any necessary moves based on that.