Only if those 161 vaccinated/infected are equally as likely to spread the virus as those in the 346 placebo/infected. You could test that by doing challenge trials I suppose where you expose uninfected people without antibodies or vaccine to people from those two groups but that would be grossly immoral to do.

Which was the point I made at the start. If the average viral load in the group of 161 was halved that would put a significant dent in the number of people they infected relative to the number of people getting infected from an infected person in the placebo group. If the infectious time was cut in half by the vaccine that would halve the number of infected.

Just because a vaccinated person has the virus does not automatically mean they will spread it as well as someone infected without the vaccine.