I've worked at companies that have been recruiting creatives and the response to a job ad can be like opening the flood gates.
In my experience a good, clear and to the point CV is a must. Be creative as a hook but at all times make it clear as these things get skim read and not always by the person that is hiring.
A good solid portfolio is the next thing. If you don't have a web-site then get a Behance profile as it's free and easy to use and you can give a direct link to the employer.
Make it EASY for them.
You'd be amazed at the poor quality of work that gets sent in so standing out that bit is key.
I've seen people send in CV's with degrees and BA's only to see work that my 11 year old could surpass.
Another big thing on applications is grammar and spelling (not my strong point).
I've often heard a director coming out of their office to rant about it.
I'd say YES. Spend the time and money on a round the world plane ticket, kick arse headphones and some pink floyd albums. Life experiences matter more in my opinion.
Self taught over here and never missed an opportunity. Turning point for me was at a masters of multi media in about 2002 and the lecturer said pre-press was not important. I left and went out on my own from there.
Nothing at school really prepares you for the reality of business, that creativity is mostly for money, deadlines means poor health, fucked off bosses are everywhere, bitchy colleges, back stabbing wankers, burnout, and that most people are mostly set on ripping you off and exploiting you.
Nothing at school really prepares you for the reality of the utter joy of great design, making amazing networks, connecting to genuine people, managing projects, helping others through creativity, solving real issues with design and also making it on your own.