Absolutely. Polio for example does not infect the nervous system in most of the cases, but in a few cases every 100 thousand people it does. And this can cause life long paralysis. Much of the fight to eradicate polio is because of this rare effect.

Contrast this to something like rabies, which always affects the nervous system (and always kills you and there is no cure, but vaccination shortly after a bite can avert that outcome).