In fact, with the arrival of a new coaching staff, he will have to adapt very well.. and very quickly.
So, not only is it a different scheme, but most of the reason the team signed him will not be a part of the scheme at all.
He has been a 3-4 outside linebacker his full career. He has mostly been in a Vic Fangio, or similar type of scheme, which is why Sean Desai really wanted to have him in Chicago. But, now that Matt Eberflus is in town, the team is switching to a 4-3 defense. This is not a significant change for some, and will actually be better for others like Robert Quinn, but for Attaochu, it will mean that massive change is coming. So, this is not the best situation for him. To start, his best skills are ones off of the ball that comes in a 3-4 scheme. He was signed to switch with Quinn at times, which kept Quinn as a hand-down pass rusher as often as possible.
As if this is not enough, the Bears would save $2.7 million if they let him go...
Here is a video of Bears analyst Harrison Graham sharing the same opinion as me: