My personal opinion is that it does. It relaxes you and soothes the brain. Unlike other music, Classical is in a class of it's own. The only music I can have on and read peacefully at the same time.
In 1962 I worked a regular night shift for Qantas and the radio station we listened to was owned by the Catholic Church. When Pope John XXIII died that year the station went into mourning and played "gloomy" music for a whole week.
Their idea of gloomy was to play the great classics. I've been listening to classical music ever since -- interspersed with lots of other stuff, of course.
Has it affected my brain? Perhaps. You only need to read a few of my answers to realise there's something whacked out in my head. Perhaps the classical music made me that way, or perhaps it stopped me getting even *shudder* worse. :(
Pretty current information: