There hasn’t been enough data collected to confirm either way as to the prevention of spread or the vaccinated person’s ability to still spread Covid-19.
The status is similar to those that are pre-symptomatic of having a Covid-19 infection. They would be able to spread the virus in water droplets but wouldn’t have a serious reaction themselves yet with contracting the virus.
This would mean that people would be asked to keep following public health safety measures until everyone is vaccinated.