Likely some, but I suspect it won't matter in terms of repoening. Lockdowns have been premised on a light at the end of the tunnel. Humans are too social to live like this indefinitely, and the virus, especially if the vaccines are only somewhat effective, will be good enough.

That said, the vaccines all seem to offer some degree of protection to the variants, naturally acquired immunity probably will too, and the virus will have to adapt to multiple vaccines and natural immunity very quickly to continue spreading.