Yes, but it seems to me that this could change the meaning a bit.
"że to zrobił", especially with specifying "że on to zrobił", can mean "that he is guilty of what they accuse him of doing". Like "I doubt he murdered her, I think he's innocent".
It can also mean I guess simply "I don't think that he did it", with 'it' that can be just 'cleaning his room'.
"czy" only has the second meaning in my opinion.