If I can add my $0.02, I've just finished my second year of a Bachelor of Arts in Political Science. My instructor told me about a student who got his CPL - that is, with no degree - at 19, and the week after obtaining his CPL, was working up in North Queensland.
My pathway is to hold both a CPL and an MECIR, as well as my BA, by the end of 2016, by which time I'll be 22.
The way I see it, if nothing else, a degree will show dedication to the completion of a task, and I think CFIs will take this into account. Not to mention I've really enjoyed my two years so far.
In Oz, at least, while a degree isn't required to work in the airlines, it's common knowledge that an airline like Qantas (if they're even around when it's time for me to apply for the airlines) wants their pilots to have a formal education outside aviation.