I think that depends on how the virus continues to circulate and how long the vaccine provides meaningful immunity. The virus itself is quite narrow in its genome - at least compared to other viruses that cause humans to get sick. If effective vaccines are deployed worldwide, it's possible that viral circulation will be so substantially degraded that it is effectively 'gone' in many places. It isn't like the flu (at least not now) where it is more of family of viruses with quite a bit of variation that requires vaccines be reformulated every year.
And, of course, if the immunity provided by the vaccine lasts for some time, that will also work to keep the virus's spread low and not require frequent reinoculation. I posted that report yesterday about new research showing the post-infection immunity appears to be very good (contrary to some earlier anecdotes about re-infection), perhaps even immunity for many years. If the vaccine does the same, that would be hugely helpful in actually eliminating the virus from circulation. Like, at all.