Not necessarily [1]. COVID vaccines particularly give you far higher neutralization titers than a prior infection.
[1] A glaring counterexample to your hypothesis is Brazil (Manuas) where prior infections (as high as 60%) didn't stop the P1 variant from ripping through.
[1] A glaring counterexample to your hypothesis is Brazil (Manuas) where prior infections (as high as 60%) didn't stop the P1 variant from ripping through.