As a former cult member, I know that certain totally wrong beliefs and intelligence are not often connected at all. A JW or a fundy Christian may not desire to be "intellectual" but otherwise, the one doesn't necessarily affect the other at all.
It can, though. A person can turn off their logic when it comes to science or when it comes to needing proof of their beliefs. But otherwise, most Bible believers seem to bathe in their cognitive dissonance. They can understand evolution as good as the next person whether they believe it or not, they can have intellectual discussions on issues or philosophies.
Before you go finding plenty of exceptions, there are plenty of exceptions in all belief systems. Plenty of people aren't much when it comes to being "intellectuals."