No.
Vaccines boost your resistance against diseases, they do *not* grant immunity. Think of it like letting a military (immune system) train against captured enemy war machines (weakened or deactivated viruses) - it grants a decided advantage in later battles, but there's still no guarantee of victory. And not everybody's military will train as quickly or effectively, nor are they all the same strength to begin with. With a good vaccine most people will be able to fight off a later infection easily enough that might not even realize they were infected, for others it will only give them a fighting chance, which may reduce the amount of permanent damage done if they survive. And for still others it just won't be enough, and will only let them die more slowly.
And that doesn't even consider the percentage of the population that legitimately can't take the vaccine, most commonly because they are allergic to certain components, or have a weakened immune system that may be overwhelmed even by the vaccine.