In addition to the degree debate, not many people want to hire someone for their first full time job. Its an obvious risk to take someone on board with no work history to look at. So if you're just wanting to cover your self for a medical loss or such, a couple years work (which realistically you'd have to do anyway unless you had some other way to pay for a CPL... or are in NZ) would be helpful too.
I worked in a factory for several years, learnt a lot of mechanical skills, learnt how to wake up every morning at 6AM, and now when I apply for a job I've got 3 years of steady employment to point to.
Not to talk down a degree... but that's a big choice to make, and one that in all honesty I wasn't ready to make at 18. Plus working a real job showed me that being a pilot was what I really wanted to do.