I voted no, but I think it's important to define what we're talking about here. If intelligence means the ability to understand music theory, then I think music with complex levels of music theory would indicate more intelligence. If intelligence means the ability to understand political or social issues, then maybe more lyrical genres like punk, folk, singer-songwriter, or rap would indicate more intelligence. If intelligence means creative intelligence, then avant garde music may be an indicator of that (since the person will likely have their own unique interpretation of that kind of music). If "intelligence" is taken literally in that the person does a lot of thinking or enjoys focusing on complex things outside of music, then relaxing ambient or study music could be an indicator.
But of course, there are exceptions to all of those correlations. Just because someone likes complex music doesn't mean they understand what's going on in it, just because someone likes music with a lyrical focus doesn't mean that said lyrics are always profound, just because someone likes avant garde music doesn't mean that they think deeply about what each element of the music means to them, & just because someone likes ambient music doesn't mean they're deep in concentration whenever they listen to it.
In writing this, I present my own definition of intelligence: the ability to understand new concepts without difficulty. From that perspective, the question of whether there's a correlation between one specific genre of music & a higher level of intelligence is "yes: a negative one", because it demonstrates an inability to learn new concepts & ideas beyond one's own already-existing understanding.
But even that conclusion has its issues. For example, if someone had absolutely zero level of critical thought (i.e. probably not very much intelligence), then they would like every type of music known to mankind. On the other hand, an inability to
enjoy other styles of music doesn't mean that someone couldn't learn about the styles' background & the appeal it has to some people. On the other other hand, just because someone isn't musically intelligent doesn't mean that they can't be intelligent in other areas of their life.
Also for the record, by my own definition, I'm a fucking idiot. 
So I think it's a personal question because intelligence can be interpreted in so many different ways, but for me, the answer is "no", because the vagueness of the question means that correlation can't be quantified in any definitive meaningful way.
TL;DR No, because intelligence covers so many different areas of the abilities of a person, & in any definition that could be correlated to certain musical styles, there will always be exceptions that don't listen to that style for the reasons you assume they do.
Poll
Topic: Is there a correlation to intelligence and listening to certain kind of music? (Read 3222 times)