Go for the degree!
Not least, many aviation managers (really just superannuated pilots or engineers, not really people who know how to manage people per se) have a superstitious awe of someone with a degree, thinking them some sort of higher being.
The degree means to them that you are hyper-intelligent and should be treated with some degree of respect. They will still crap on you, just not from such a great height!
Also, as pointed out here, once the gloss goes off flying for living (hard to believe but you can have enough of it after a while) having a degree makes it so much easier to find other work.
You might want to keep quiet about the degree, assuming you have one, for certain bottom-feeder jobs, though. There the manager's looking for a certain degree of desperation, what he's comfortable with, people lower on the evolutionary scale than he is. (Think: the sort of green scum you see on the glass of your aquarium.)
It's so much easier to do the degree now, before you get involved in that frantic quest to build hours and climb the greasy pole. You will never have this sort of free time again so that the time to do the degree is now.