Can a person be infected with Polio even after vaccination in childhood?
Short answer: Yes.

Slightly longer answer:
Recall how a vaccine works - it introduces an antigen to the body, which provokes the body to produce antibodies towards that antigen. 

Antibodies, simply explained, call upon the remainder of the immune system to fight off a potential infection of foreign body. If there is no immune system to mobilize, the infection would most likely run its course. However, the immune system would have to be sufficiently weakened in order to not be able to fight the infection.