Obviously the Bulls aren't going to be better off without Noah. They'll be hurt by the lack of depth. They'll miss his rebounding, help defense, and hustle. However, all is not lost. Not even close. The Bulls have quality depth to get through this period, and they'll better develop Asik through the process. Also, they aren't exactly facing the stiffest of competition over this stretch.
Assuming Noah is gone for 10 weeks, and we'll assume he has surgery in the next few days sometime. He'll be out roughly until the end of February. For the sake of argument, we'll assume a March 2nd date against the Hawks is the game he comes back in.
The Bulls will play 35 games over that stretch. That seems pretty gloomy. However, looking at the schedule closely, and the Bulls will be favored (even without Noah) in the vast majority of these games.
In fact, the only games the Bulls will likely be underdogs in are the following:
Jan 8 Boston
Jan 15 Miami
Jan 20 Dallas
Jan 28 Orlando
Feb 7 @Portland
Feb 9 @Utah
Feb 12 @New Orleans
Feb 17 San Antonio
Feb 24 Miami
That's 9 games, most of which are at home, and the game against Portland the Bulls still might have the advantage in. That leaves the Bulls as favorites in the other 26 games.
So the injury hurts, but it doesn't doom the season as it comes in a soft part of the schedule. It's a good time for him to have the surgery as it gives him time to get healthy for the playoffs and to integrate with the team again once he's back.
While Noah is out, the real question will be how the Bulls manage the starting lineup. They could start Boozer/Gibson and then bring Asik off the bench and utilize small ball more which is what I expect. There's also some chance they start Asik and continue to bring Gibson off the bench against teams with legit size.
Kurt Thomas could be in the mix, but he's been awful so far in very limited time which is why I expect the small ball lineup with Asik getting a large minute increase being the most likely scenario.