Yes but very rare though, he really has bad luck if he’s vaccinated and still caught it
It wasn't rare that you could catch it. For the trail period they only check for symptoms and the severity, which confirmed their efficacy. Now that more have been vaccinated, they've been discovered that you could still catch it...and are now really using the population to test how transmissible it is from the vaccinated. All the vaccine did was mimic the attributes of those that were truly asymptomatic (those whose bodies fought it off without ever even knowing they had it).
Which strikes me as strange with Chris Paul is that if there is no testing for vaccinated (they don't really care if you have it, since you won't get life threatening symptoms, if at all) is that he may have been exhibiting symptoms, and that's what prompted this entire thing. If that's the case, he truly is cursed.