Yes, but the chances are much lower than someone that's not vaccinated. The risk level is explained in more detail here, but here's the gist: "Basically, whatever rate of the population is getting COVID-19 now, a population fully vaccinated by the Pfizer and Moderna vaccines would have a rate 95% lower and a population fully vaccinated by the Johnson & Johnson vaccine would have a rate 66% lower."

Also, the people are asymptomatic. There's a good chance they wouldn't be if they didn't get vaccinated.