I certainly agree with you in the sense that if a line grunt has no faith or respect for their CIC and his chain of command, then any decisions by the CIC that directly affect said personnel in a very direct and existential way is going to be met with less than a full commitment that is needed to accomplish any missions passed down the chain.
I agree with the sentiment that ultimately it comes down to fighting to keep yourself, the guys next to you and the unit's ability to see the sunrise the following day and the ones thereafter, but having no faith or even disgust for the CIC and his agenda absolutely has an effect on unit morale, unit integrity and personal convictions.