It wont cure current infections or help them in anyway, but it will prevent from a couple other common ones (high and low risk) so it may be useful to you, to prevent you from getting any more and making your condition a little more annoying
Yes, the vaccine is preventative. It might not (i am not sure, but my guess is it doesn't) help cure current infections.
But it protects against 4 specific stains of HPV. You may have one of these, but it is also possible that you haven't been exposed to any of the strains covered by the vaccine.
These types of HPV are responsible for 90% of genital warts and 70% of cervical cancers. Your doctor probably sees this as a good way to protect against future infections.