Agree with soccerguy that level of interest is not considered as an admissions criterion at W & M - we did a total of 4 tours with 3 kids, and that point was expressed each time.

However, the interview for rising high school seniors can be an admissions boost. As Ronbo1960 mentions above, the interviews are done by W & M students (I believe they're all rising seniors?) who work in W & M admissions. The interviews are not mandatory, but they are evaluative. So if your child is interested in W & M and likely to score well in a personal interview situation, a good time to visit would be during the 5-6 summer weeks that interviews are offered. The student won't make points by showing up for the interview/tour, but they can stand out from the crowd with a successful interview. Since so many statistically qualified kids apply to W & M, the interview is a good idea unless the student is reluctant (maybe shy or socially awkward?).
If I remember correctly, rising seniors can schedule an interview beginning May 1st. They're only held during part of the summer, and there aren't enough slots for everyone who wants one.
My youngest d, now a sophomore, interviewed and enjoyed the experience. We think it had to have helped - her GPA was in the A-minus range (with a rigorous curriculum, but still), which is not outstanding for OOS female applicants. It couldn't have hurt, anyway.