Not really, no. A person with a degree from a prestigious school is likely to be smarter than a person selected at random from the population, sure. But that doesn't mean they should be deferred to in areas where they lack knowledge and experience, and never automatically.

That said, we all get to deal with the world as it is, not as it should be, and an Ivy degree is a pretty nice perk. It seems a shame to toss it away if there are other ways to deal with your depression.