If a child is vaccinated for chickenpox but she gets the disease anyway, will her vaccination affect the likelihood of transmitting the disease to others?
From the CDC report:
Communicability The period of communicability extends from 1 to 2 days before the onset of rash until lesions have formed crusts. Vaccinated persons with varicella may develop lesions that do not crust (macules and papules only). Isolation guidance for these persons is to exclude until no new lesions appear within a 24-hour period. Immunocompromised patients with varicella are probably contagious during the entire period new lesions are appearing. The virus has not been isolated from crusted lesions.
Varicella is highly contagious. It is less contagious than measles, but more so than mumps and rubella. Secondary attack rates among susceptible household contacts of persons with varicella are as high as 90% (that is, 9 of 10 susceptible household contacts of persons with varicella will become infected).
So, vaccinated people with breakthrough varicella (infection despite vaccination) can still be contagious. The duration and severity of their syptoms tend to be reduced, which leads to the issue mentioned above where you cannot rely on the crusting of lesions to determine when they are no longer contagious.
In clinical trials, breakthrough varicella was substantially less severe with the median number of skin lesions commonly less than 50; vesicular lesions are less common and the lesions are commonly papules that do not progress to vesicles. Varicella in vaccinated persons is typically shorter in duration and has a lower incidence of fever than in unvaccinated persons.
On the plus side, they are overall less contagious if they have the reduced symptoms:
One study of varicella transmission in household settings found that persons with mild breakthrough varicella (< 50 lesions) were one third as contagious as unvaccinated persons with varicella. However, persons with breakthrough varicella with 50 or more lesions were just as contagious as unvaccinated persons.