No, Barb controls Chris through some fucked up emotional, and almost physical intimidation. If she needs Chris to do something, either he does it or someone's going to jail.
I think that Chris has the human desperation in him to do his best job maintaining it. He might fuck up one or two jobs, but he seriously isn't going to mess up a third. Barb would either believe Chris' excuse about why he got fired, fight the manager and go to jail, or she'd flip out at Chris and something bad would happen.
Seriously, if Barb's back's against the wall, she's not going to let Chris fail.