Only if you assume (1) perfectly homogeneous mixing and (2) nobody is naturally immune (either due to cross-reactivity with immune responses to other coronaviruses or for any other reason).
Currently the effective reproduction number is not 3, in most places, because we're avoiding large gatherings and, depending on the region, wearing masks and avoiding indoor gatherings.
If many more people were immune, even if we hadn't reached herd immunity, we could safely relax restrictions on gatherings without causing another wave. Concerts would still be out of the question, but dinner parties and hair salons would no longer be so concerning.
So vaccinated people will not get too sick, not self-isolate, but will still shed the virus? That sounds concerning for the non-vaccinated.
[] ChAdOx1 nCoV-19 vaccination prevents SARS-CoV-2 pneumonia in rhesus macaques