In most cases yes. But when we're talking about elite colleges, it has significant bearing. Living in the dorm with a future CEO may be helpful in your future job search, and if you go to an elite college, you have a much better chance of having done that.
Going to Stanford or Berkeley or MIT or UW and doing CS there will mean that when you graduate, a whole lot of hiring managers will see that you attended the same college they did and give you an automatic boost.
And if you go to USC film school, you're pretty much guaranteed to know someone who will one day be very successful in the film industry and will help you get jobs or connections to have your own projects produced. Heck, the school does that for you.
So yeah, in most cases it doesn't matter, but in some very specific cases it does.