At some point this is just arguing semantics, but my understanding is that the herd immunity threshold is defined when Reff < 1. You could have Reff=0.99999999, which counts as herd immunity being reached, but it would take a very long time for the virus to actually disappear. Even if we do momentarily hit Reff < 1 for the delta variant, there could be mutations/waning immunity that causes it to stay around 1 becoming endemic.
No, it is impossible to reach herd immunity if Reff >= 1, but Reff < 1 is not sufficient for herd immunity. Herd immunity also means low enough incidence that a nonimmune person is not at significantly greater risk than an immune person.
Herd immunity would usually be defined as: if a contagion is introduced to a community will it spread uncontrolled or will it die off. Reff < 1 implies it will die off, Reff > 1 implies it will spread. Herd immunity does not mean that the contagion is not present within the community or anything about the relative risk between immune/non-immune community members.
