Noah is one of the best (and plausible) acquisitions this team can make... at the right price.
Depending on what direction the franchise wants to move in and what occurs during the season, I can see Chicago moving on from Noah. They have a depth of talent that goes at least 2-deep at the 3-4-5:
Gasol - Noah - Portis
Noah - Gibson - Mirotic - McDermott - Portis
Dunleavy - Mirotic - McDermott
The Gasol-Noah pairing hasn't worked out as expected; I can foresee a situation, where one of the young players on the roster displays that he is ready for a starting role, is a better fit alongside Gasol, and will be under team control for the foreseeable future. They aren't going to pay Noah and Gibson (based on a notoriously frugal front office), and Noah's injury history and age might make him the odd man out (he might command a higher salary than Taj on the open market despite his age and injury history).
A deal where Chicago can gain valuable (cheap) pieces (a.k.a potential lottery picks) in exchange for half of a season of Noah would do it; and if he likes the team and the contract offered matches what's offered on the market, I think he would be likely to stay. I would trade the Mavericks 1st or Young and Grizzlies 1st (+ salary filler/Jerebko) for Noah.