I have heard with the speeds of those planes, especially at altitude that they are nearly impossible to hand-fly and keep passengers happy.
Unless you are getting a very specialized degree (engineering etc. ) then having a degree gets you into the door at a number of places. There are many people out there with degrees that aren't in their field of study. With that being said, if it would save you money to do an aviation degree go for it. If it were me, I would do a fast track program and get your CFI so you can make money and build hours while your working on school. And remember, a Bachelors's degree isn't mandatory till the Majors( and not necessarily mandatory then either), you could be working on said degree while you are CFI'ing, corporate flying, freighting, regionals etc.
This is coming from a person that got my B.S. in Aviation Management 8 years prior to finally getting my commercial license, I ran out of money for flight school way back when and was out of aviation for 8 years. If i did it the other way I would be in a much different position than I am now. I would of most likely been a captain at a regional by now, where as of now, i am just completing my CFI's at the age of 32 and wasted the past 8 years of my life bartending and serving tables. I am not bitter, just happy I am finally here. Take it for what its worth, good luck!!