This is incredibly wrong.
Evolution is incremental. To become vaccine evading, the virus has to have a host it can replicate it, and a host that is a resistant target.
In fact it needs a big pool of them, since once infected develop immunity they no longer produce trial mutations.
So you need a pool of the unvaccinated, coming into frequently, regular contact with the vaccinated in order for any specific vaccine escape to evolve.
This is because, any incremental improvement needs to become a population dominant strain within the unvaccinated population: that you survived in a vaccinated person for a little bit is irrelevant if at the end of the day every virus with that trait dies without spreading.
Even if you successfully do spread from a vaccinated host, you need to either land in another vaccinated host (who then spreads you around: so isolation measures are effective), and while you're doing this you need to develop a better escape system: not guaranteed, because if overall viral loading or time to immunity is shorter, that's less time to generate variants.
But...a good way to optimize this, is to just spread to a pool of unvaccinated people. With luck you retain the vaccine-escape mutations, become dominant within the unvaccinated pool, and then get lots of opportunities to try and infect vaccinated people and get a little further.
This, incidentally, why viral evolution tends to consist of "the virus jumped between species several times" - because crossing a species barrier requires ongoing persistent contact between a host you can replicate it, and one you're trying to cross over into.