Let’s settle this since this message seems to be very convoluted. It’s unlikely. There is a difference between a carrier and a transmitter. Vaccinated individuals can get infected and carry the virus. What is important to know is the viral load is so low you can’t transmit it. https://twitter.com/apoorva_nyc/status/1377762957417799684

Spread/transmission therefore is blocked and we can proceed to a pandemic exit strategy. FWIW, vaccinated people who do get infected tend to only have mild or even asymptomatic cases of COVID-19, and don’t require hospitalization. This means the vaccines are indeed working.

I say this because I feel the message gets lost and it can easily begin to promote vaccine hesitancy. Most individuals will ask “Why should I get vaccinated if it doesn’t do XYZ?” When things like this can be remedied simply by breaking it down and explaining it.

For more on real-world data on vaccine effectiveness as well as transmission data in reference to my points made above please see: CDC Science Brief: Background Rationale and Evidence for Public Health Recommendations for Fully Vaccinated People
https://www.cdc.gov/coronavirus/2019-ncov/science/science-briefs/fully-vaccinated-people.html