Think practical for a minute... when the airlines start requiring an aviation specific degree, then look at getting one. Until then, I believe you're foolish to not diversify. Getting furloughed as a pilot at some point in your career is fairly probable. You like to work? Then have a backup plan. ERAU, UND or the other "aviation colleges" don't publish their back-up plans, do they? You gonna get hired at ExxonMobil with an aviation mgmt degree? How about GM? IBM? Merck? think about it.
Get a degree in business, engineering or anything in the medical field from an accredited school.
Regarding the aviation degree in engineering - I assume you're talking about aerospace engineering. If that's absolutely what you have to have - fine. Good luck. If you want to work in the aerospace field (unless highly specialized) you can get hired with a mechanical engr degree. So when the particular project you're working on get's cut - as happens frequently - you can take your ME degree and go to work in engineering & contruction, manufacturing, semiconductors, energy, etc, etc.
After rereading the post above from abatista, I got the impression that their point was to get some aviation information or education in an engineering program. About the only thing similar between any accredited engr program and an "aviation degree" would be History 101, Economics 101, English 101... From there on, the engr coursework is almost totally analytical - calculus, physics, chemistry, mechanisms, controls, materials, fluid mechanics, thermodynamics, design. Nothing in any engr curriculum I'm familiar with would come close to how to running a flying business, managing a group of pilots, aviation regulations or similar.