a yes and no...
First off, Steveash hits the nail on the head...
we live in an odd time where many connection attempts just get immediately round-filed. To that end I would suggest you not go the email or mail route, at least at first. Go old school, pick up the phone, or try and stop over in person (which is probably the hardest thing to time, since most studios will be far to busy to deal with unplanned distractions). Make a first connection as not looking for anything more than advice. Come clean, and say you are interested in the field and want to know how to get started. Many designers will gladly share advice with someone who is trying to get started.
As far as formal design schooling... I have been an art director and designer for over 27 years now. 17 of them working for a company, and now 11 years on my own running a design studio. I went to school for art history, by the way. Go to school. A good education should teach you how to think clearly and to write well. Specific software platforms & skills taught in schools are mostly a waste, as they will be obsolete the day you learn them. A design or typography course would not hurt though...
I learned everything on the fly, by myself, and taught by some sage souls along the way. It is way easier now too... with tons of good technical schooling options like Lynda.com, etc. Learning how to learn is a key skill, as the technical skills you will need will continuously change.
The field can be lucrative for some. For many it is a tough road though, as there has been a trend among ad agencies to fire most of their creative staffers and rehire them as freelancers (how classy). Most agencies I know run a mean & lean ship, and have collaborations with other professionals that they can bring together on a project basis.
Seek an internship, or unpaid position, where you can pick the brains of the brightest minds you can find. Ask a lot of questions, and never say no to what is asked of you (work related). Watch and learn, and then decide if it is for you, or not.
Build a body of real work, not fake stuff. It is actually easier than you think, as there are always folks looking for "free" work. Be selective when choosing your clients (even if they don't pay).
There is a good short book by the principal of Mule Design called "Design is a Job" (
http://www.abookapart.com/products/design-is-a-job/). It is a short but good read that covers most things you would want to know (including how to fake it when you are getting started, and how even crappy jobs can teach you valuable skills, like speed). It is a book I wish I had read when I was younger, and find the advice spot on.
best of luck to you,
michael