Does what you listen to affect your thought processes? Yes.
Is there any way that any particular classification of music makes you either smarter or not?
I will grant that it makes an interesting hypothesis for neuroscience geeks... but like anthropogenic global warming and the Piltdown man it is just so much self justifying hokum.
The capacity to appreciate any kind of music or art comes from the human ability to recognize patterns. Intelligence provides us with the tools to see patterns like those in music and in addition, to interpret and predict how those patterns will progress. In turn we experience changes in the perceived pattern of events in music with varying degrees of surprise which on turn may cause confusion or a sense of pleasure.
And so it is that depending on your mental flexibility you may be either pleased or disconcerted by different types of music.
One thing for sure is that the more intelligent you are, the more likely you are to truly appreciate music of any kind. Anyone can appreciate music but it takes more than just passive experience of the sound to really get it. The more you listen, the more you use your interpretive skills whether consciously or not. And so, listening to music, classical or any kind does exercise the mental tools you already have. It certainly does not make you smarter.
Smart people do get classical music. People pretending to be smart do not. At least not in the way they think or would like you to believe. Generally, these people can be recognized as musical snobs.
But, listening to jazz or classical or whatever is never going to make anyone smarter than they already are. By the same token, a lot of very smart people get a lot of pleasure from music that the snobs hold in disdain.
Which brings me to the idea of teaching music to children as a means of increasing their intelligence.
One of the most ass backwards ideas I ever heard of. Because, it is good to exercise young brains and young minds will respond to being exercised does not make it right to assume that this makes them smarter. Every child should be afforded the opportunity to learn music. Not every child will benefit in the same proportion from the experience.