140 million vaccinated (approx the number of flu vaccinations administered last year) + tens of millions with natural immunity does put us close to the herd immunity threshold (the number of people that have immunity from an infection has big error bars of course, and there will likely be overlap)
Also, acquired immunity might not be forever. Could be possible to get reinfected.
And you have a very optimistic understanding of how many vaccines can be manufactured and distributed, I would guess.
Distributed, probably so. I don't see any reason to doubt the manufacturers statements yet, and I'm not including the potential/likely J&J vaccine.
And while we don't know how long acquired immunity lasts, it's pretty clear that it lasts a good while (it's still a freak occurrence when someone tests positive after recovering from a first infection).
Unfortunately a PCR result at a 35 cycle threshold (which the vast majority of tests in the U.S. are) does not prove that a person was infected and has immunity, only that there was exposure that is detectable. It may never even have entered the bloodstream.
Only antibody testing will show if there was a immune response and if there is immune memory. We're not doing that at scale.