Oranj: The point system isn't exactly the way you might think it is. There are 3 general categories. In those categories, everything falls into. The three categories are:
1. Academics: 60% of your total score. It includes: Academic Composite High School or College academic performance, SAT or ACT scores. It can be somewhat subjective because of school profile, difficulty of classes, weighting of classes/grades, class ranking, etc....
2. Leadership/EC/Athletics: 20% of your total score. It includes: Extracurricular Composite, Athletic participation, leadership position (scouts, school clubs, class officer, etc.), public/community involvement and work experiences. This too can be somewhat subjective. Were you just in scouts, or an eagle. Were you just in football or an all-state/captain/etc... Were you just in band or a section leader. Were you just in CAP or did you receive certain awards or recommendations like in your situation.
3. Administrative in nature: 20% of your total score. It includes: Admissions Panel Faculty and staff review, candidate fitness assessment, Admissions Liaison Officer interview, and writing sample. This can also be subjective. No two teachers recommendations will be the same. No two ALO's are the same.
So yes, your recommendation will definitely give you more points in the Leadership category compared to someone who was in CAP and didn't receive that recommendation. But what if there is another CAP applicant you are competing with who on the sports side of that same category was ALL-State, ALL-Conference, and Captain of the football team; and you were on the team and didn't have that extra. Do you think your EXTRA in CAP (Recommendation) might be a wash with their EXTRA in Football for being the captain?
Do you see now how it's impossible to say the AMOUNT of AFFECT these awards, accolades, achievements, etc... provide.
I will tell you with 100% certainty, that the recommendation gives YOU, and YOU ALONE, more points than you would have had if you didn't receive the award. Now; is that enough to receive an appointment? No one here knows, because we don't know all your points or the points of your competition.
Now; Packer brought up the additional factor of the Prep-School. The academy definitely uses such recommendations in their decision in offering prep-school slots. But remember, prep-school is designed traditionally for those applicants who other than an academic area, are excellent candidates. If you happen to be a stellar candidate academically, then there is a slim chance you'd be offered a prep-school slot. But a stellar candidate academically, excelling in CAP (With your recommendation), etc... is definitely (COMPETITIVE). And that's the true word you should be thinking. The recommendation makes you MORE COMPETITIVE. How much more? Hard to say. I had an individual ask me if finishing all high school requirements a year early; holding a 3.98-3.99gpa; 31+ACT scores; and taking ALL COLLEGE classes in their senior year would make them extremely competitive. I definitely thought so. "At First". Until I realized they had NO SPORTS and very little leadership.
Hopefully you can see how difficult of a question you are trying to ask. We know nothing else about your resume/application; we know nothing about your competition; and you want to know if getting this recommendation will affect your chances of receiving an appointment. Well YEA, it will. So will being in the band, scouts, soccer team, chess club, etc... How much it affects it,,,,, no one can tell you that. Even saying it helps a lot is misguided. Sorry for the novel, but your question isn't simple, and the answer isn't simple.