We can answer the question, but we haven't yet.

Scientists did an incredible job of developing an effective vaccince in roughly 1-year. That process usually takes 3 or 4 years.

To do so, the clinical trials were focused solely on safety and efficacy against illness. They did not study transmission. It is being studied now so that we will have an answer. Until we do, or until herd immunity is reached, reasonable precautions are sensible.

The link is from Johns Hopkins. Paragraph 7 addresses your question directly.

Click here for link at https://coronavirus.jhu.edu/vaccines/vaccines-faq