One other note: being offered a CVW is typically a good sign. I would say a better sign than NASS (which is a recruiting tool). However, CVW is NOT a guarantee of an appointment. [And, no, I don't know the percentage of those offered CVW who are offered an appointment.
] The goal of CVW is to let well-qualified candidates experience USNA while school is in session, so to speak.
If you are offered the opportunity -- regardless of whether you attended NASS -- you should take it because it is yet another way to ensure that USNA is right -- or isn't right -- for you.
For many candidates, CVW may interfere with sports or other ECAs. If you choose not to accept CVW, it will NOT hurt you from an admissions standpoint. However, IMO, it's not a wise move to turn down a CVW unless you cannot financially afford to make the trip (which is a valid reason). Why?
This is your potential future. If you accept an appointment, this is where you'll be and this is what you'll be doing for the next four years of your life and, in joining the military, at least the next 9. Be sure it's what you want. Take advantage of every chance to challenge your beliefs. While h.s. activities and commitments are very important now, they all pale in the long run in light of your future.