In a sense no, hence the choice to vaccinate younger children who will mostly not be sexually active yet.

But because the modern versions of these vaccines cover many strains (initial vaccines were two, Denmark chose a 4 way vaccine, now a nine way) it's very possible that you get a meaningful benefit by being protected from say six strains your body has never seen, even though the three it has already seen wouldn't be prevented.

It should be noted that the decision to vaccinate younger children is a combination of disease prevention and cost, not just vaccine effectiveness.