Yes, having been in the military and having researched some of the opportunities within, there are far more important things, like promotion points, PT tests, being a "rounded" candidate as the others are mentioning. They looked at transcripts and test scores, not so much the degree. I'd assume it would matter the least if you were already "in" the military, maybe slightly more if you are looking at going directly into an OCS/officer program from the get-go, but you are essentially looking for a pilot slot, there is so much more that goes into this, can you pass the physical? What about later? What about later at the airline? What about when you get furloughed from your airline? What do you do then? If you like aviation, then get a degree that is related but not so dependent on everything else in your life going perfectly. An aviation science degree is basically putting all your cards on the table and hoping it works out in the end, and if it doesn't, you end up absolutely screwed. There is no "science" to it, it's the things you learn going through pilot training, on the line, etc. It doesn't help you do the job better. Do you ever want to be a test pilot for the military or an aircraft manufacturer? Chief pilot for a major airline? Get an aeronautical engineering degree, or get a degree in industrial safety, or human factors/ergonomics, or psychology, or accounting, or business management, or one of many other far more helpful areas that would still apply to things outside of piloting. There are many ways to be involved in aviation, way more than most people ever really include, there are less ways to be a pilot and involved in aviation, there are even less ways to be a commercial airline pilot, and there are only a few ways to be a pilot for a major commercial airline, and past that VERY few ways to be an international major airline commercial pilot. Look at it from the other way, if you look past just being a "commercial pilot for a major airline" you can maybe see the forest for the trees, and that's kind of what you need to plan for in this industry. If you bet all your chips on that one route, you might end up at 40 years old flying for a regional making $30k/yr for several years and might get "stuck" in a down cycle or furloughed. Wouldn't it be nice to be able to choose a different career, get on with boeing designing airplanes, manage a 135 operation or something else if things don't go perfectly? And if they do go perfectly, the degrees mentioned above will take you at least as far, if not further, than an "aviation science" degree.
If you still think you might "need it", then wait until you are in the military and do your master's in aviation-something. A HUGE percentage of military folks do this, it's one of the driving factors keeping schools like Embry-Riddle in business, through on-line and worldwide (at bases) campuses, because officers need Master's degrees eventually for serious consideration of advancement, so this is when most of those pilot-types get an "aviation" degree, although it's mostly to check the "master's degree" box, because truly advanced engineering and other "science" degrees are much more hard work, but that's hard work that pays off (test pilot stuff, design, engineering, etc).
My 2 cents.