The programs are general in nature, unless there's some specific theme that Greg Everett lists. Since you're endeavoring on the strength-building block, you're focusing on strength for weightlifting. So, if you want to get stronger in your weightlifting movements, then you're on the right path.
With that said, it's important to point out that these are the base movements to get stronger for weightlifting; that is, should you execute the program, you will get stronger in your squat, snatch, clean, and jerk, but there are other facets that you might need to address based on your needs and what you listed. If you want to continue bodybuilding, you might want to look at your schedule and how you're going to fit all the work in. Ask yourself this: are you starting the cycle to be a better weightlifter, or for the aesthetics? Do you like portions of the program, or do you want to do all of it and then try to fit in bodybuilding?
The type of hypertrophy you're going to get from your bodybuilding is different from what you'll gain by following the CA program; again, they're totally different focuses. That's not to say that bodybuilding isn't important for general wellness. In fact, bodybuilding helps prevent some injuries (e.g., biceps curls for elbow ligament health, tricep extensions for increased confidence in the overhead position, incline bench press for shoulder joint health, just to name a few). It's going to be important to manage that soreness you'll get from bodybuilding pumps.
Personally, I think you should rank order what's most important to you and modify the program to best suit your needs. If you just like working cleans and want to get better at them while increasing your bench, deadlift, and overall body measurements, then portions of this program will work for you. In the end, you have to make the program work for you.
I hope that wasn't confusing. If it was, I'll be more than happy to take another stab at it.
Javier A. Sanjuan
Olympus Barbell Club
Dear God, please help me lift heavy and be awesome. Thanks. Amen.