"Aside from the obvious advantage of having a top-notch degree in most industries, is an Ivy League degree going to give me an advantage over pilots with lesser degrees in the airline hiring process"

No

Nobody cares where you get your degree or what it's in. Nobody cares what flight school you went to, either. A non-aviation degree in an area that interests you is best. If you did decide on an aviation degree, there is a small, relatively inexpensive, program at Central Washington U in Ellensburg. WA and OR have an agreement to waive out of state tuition fees.

If you ever get up to Spokane, track me down and I'll give you a ride in my 152.