Absolutely not. There's so many factors that go into this. Many doctors are choosing not to carry gardasil because of it's sheer cost- it's expensive, very much so. Second, by making it mandatory, it's taking away the family and -girls- choice in their sexual activity, and essentially saying "well, society expects you to be having sex anyways, so lets give you this vaccine which will offer a false sense of security" Teens are so rarely educated about sex, and that needs to come first- my cousin was dead convinced that giving a blow job could make her pregnant, but never considered an STD.
From the side that doesn't include the morals, the vaccine itself is, at best, questionable. The efficacy of gardasil in 9- to 15-year-old girls is inferred. We do not know how -long- gardasil works, as it's only been studied for 2-4 years. In theory, a 16 year old girl could then be at risk for HPV if she got the vaccine at 9. We don't yet have the long-term information.
Within the 2-4 year period, it was not effective in preventing all cases of cervical dysplasia or genital warts. Gardasil did have some nasty side affects for a "favorable" amount of people. Yes, that does mean they're fairly uncommon, but -someone- has to be in the unfortunate 10%.
gardasil can be a good choice for some women, and it certainly has alot it can be praised for thus far. However, it has many downsides and that's why I feel it has no place being mandatory in schools- if a girl shouldn't be at risk of transmitting it at school (ie, having sex there), then there is absolutely no reason for her to have to get it to -be in school-.