I voted 'yes,' classical music is still relevant in today's culture. Isn't that why it has the name "classical" and is deemed as "classic?!"
For me, classical music is still the backbone of music theory and practice in a variety of genres. Many noteworthy musicians are classically trained (some are not, and I don't have a problem with this) but the fact that most are means that there origins will have some kind of influence in the music they create.
Not to mention, much of the music created today includes practice that was prominent in classical music - the cycle of fifths, scales, arpeggios, time signatures, etc. It's not entirely obvious but all of these defining features, I believe, still seep into music that is constructed today.
Not to mention the fact that people still listen to classical music. All the time, every day. In fact, classical music is still one of the most popular musical genres. Doesn't that just go to show that it is far from becoming irrelevant?
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