NO. There is a big difference between germline and somatic mutations. As to could it? While not physically impossible, all we know about how vaccines work and how mutations occur tell us that it is as close to impossible as you can get w/o actually getting there.
Wong Grz, the term adaptation doesn't mean what you think it does. In this case there is no genetic adaptation to diet. There are epigenetic changes brought on by specific things but this is not an adaptation as we define it.