Regarding the CIC, or any other governance structure, much of the effectiveness or otherwise is down to how it is operated and who operates it within the framework in place. In other words the professionalism and capabilities of the officers are generally more important.
Strategically however, the CIC may have an impact for good and bad. If the engagement of fans can be improved by the operation of a well structured and operate CIC then the club will generally benefit. Where it may have a negative impact is in the attraction of external funding if those who are of a mind look at the lack of influence they would have and decide it is not for them. Not every funder wants the same thing, but putting money into a system that allows them little say on how their money is spent is likely to be less attractive than where they can take a notable shareholding for example.
All of which is a moot point if you have the right manager, appropriate players and a good match day experience. Get that right and the rest follows.