Personally, I think the two greatest benefits of CAP were drill and ceremonies and the application process. Drill and ceremonies is pretty self-explanatory. Knowing the basics of marching, customs, and courtesies pays off at the beginning of basic. Everyone gets to the same level very quickly, but it's a little less stress in a very stressful environment. The first couple days are the hardest due to the whole new environment. Therefore, I'd say it just helped make the transition easier.
More importantly, CAP is great during the application process. It looks great on a resume and shows interest in the AF. As well, it provides at least some insight into the military world. As well, a job like Squad Comm will show a capability to lead. Nonetheless, CAP alone won't get anyone into the academy, but that's not a surprise. Lots of people here have a CAP background. In the end, it's another little boost but one that is looked upon fairly highly (especially if you are higher up in the system). HOWEVER, I've always heard the advice that upon receiving an appointment one should keep CAP fairly quiet. Be proud of your accomplishments but don't flaunt CAP. It's a totally different world and some cadets aren't necessarily supporters of the program. Yet, many are. If it's important to you, don't hide that aspect of your life from squad mates but do hide it from cadre.