Not if contagious! Chicken pox is highly contagious and is spread very easily in closed in areas. The virus will be recirculated in the a/c system. So no.
Chicken pox. Usually chicken pox is contagious for the first week that they are sick. The actual rash doesn't show up for the first 2 days, so usually you are walking around feeling a little sick, but don't know you are contagious with chicken pox because you haven't broken out yet. Once the pox are scabs, then you're not contagious any more.
I would not... ...Bring a child with chickenpox on an airplane. She could infect any passenger who hasn't had it or been vaccinated against it. More importantly, a very elderly passenger, or one with a defective immune system, could develop chickenpox pneumonia, which is potentially fatal. I would not take a chance like that if she were my child.