Could a human become infected with rabies in such a way that even prior vaccination wouldn't stop the infection?
Reframing your question as:


  Are rabies exposures at specific sites on the body riskier than other sites, even for a vaccinated individual? 


Possibly for post exposure prophylaxis, but probably not for pre exposure vaccination. 

Rabies transmitted by a bite or scratch (almost all cases) involves a period of slow replication in muscle tissue at the site of the bite or scratch (see Murray Medical Microbiology Ch. 60 for a general discussion). This is called the incubation phase, and it is highly variable. The incubation phase is followed by a prodrome phase (virus binds receptors of sensory neurons at the site of exposure, and travels to the CNS) and neurological phase (infection of the brain). 

An effective immune response is believed to be the result of both an antibody response and cell mediated immunity during the prodrome phase. Post exposure vaccination is effective because the incubation period provides enough time for a naive immune system to mount a protective response (same reference). Regardless, rabies post exposure prophylaxis (PEP) includes both active and passive immunization, i.e., vaccine and human rabies immune globulin. 

Both post and pre-exposure prophylaxis failures have been reported. As discussed here cases with pre-exposure vaccination failure involve immunocompromised individuals. Cases with post-exposure prophylaxis tend to involve failure to fully follow guidelines (some are summarized here), but there is a recent case where guidelines were followed. These cases tend to involve bites or scratches to the head and face, which tend to involve a more rapid progression from incubation through prodrome to the neurological phase.

So, since reports of post exposure prophylaxis failure tend to involve specific locations of exposure (head and face), it's reasonable to assume that an exposure there has a higher risk. There is no data supporting this risk for cases with pre-exposure vaccination.