No, herd immunity means "enough people are resistant so the vulnerable ones don't get infection spread to them at all". There's a big difference there.
Enough people are resistant so instead of becoming virus factories and spread it further they stop the infection with their immune system.
If most of the people are immune, the fire has no combustible to propagate and it stops.
The level at which this happens depends on the ease at which the virus spreads. If it spreads easily, herd immunity kicks in much later than in the reverse case.
But the degree and duration of immunity that usually follows SARS-nCoV-2 infection isn't well established yet, and coronaviruses in general are noted for not producing lasting immunity.