The USA and a few parts of the far/middle east like airline pilots to have a degree. They really don't care what the degree is in, or how good.
There are some specialist jobs where a degree, preferably a technical degree, are of significant value to you. They are flight test, and a lot of armed services: a very large proportion of military pilots have good degrees. Those aiming for management pilot positions in the airlines do well do to a management degree of some form.
In Europe, nobody cares if you have a degree if you are *only* a civilian pilot - it's all about your flying qualifications, experience and reputation - anything else is unimportant here (actually once you have the job, the same's true in the USA as well). Where you fly for a European airline is completely irrelevant - if you have an EASA licence, and you're flying a European registered aeroplane, you can fly anywhere in the world and nobody will care about your educational background.
As I've said on here a few times, I am one of those oddballs who have professional engineering AND flying qualifications. That has opened the way to some fantastic jobs, but they're all very nonstandard. That suits me - I would hate to either fly the standard scheduled routes, or do a conventional design office engineering job. Many people however are much happier in the mainstream.
In most cases, Paco is right that it's not a backup. The exception, maybe, is that if you did an aero-eng degree, then time flying would be regarded by most recruiters as valuable industry experience. Any other degree, probably not.
A real backup would be something that allows you to earn money quickly - short order chef, plumber, personal trainer... But that may not suit your personal ambitions, which is fair enough.