A couple of thoughts. Higher education can never hurt. For you personally, it exposes you to field(s) of study that might prove useful if your aviation career flops -- whatever those reasons might be. Also, it shows the airlines during your interview that you have the dedication to earn an advanced degree, and that you have the smarts to keep that degree in your back pocket for future use in case you're out of a flying job.

I realize your question pertains to the majors, but when I interviewed for the regional where I was hired, one of the check airman asked me if my MBA meant that I was going to be bored stiff sitting on my butt as an FO. I guess he thought maybe I was a bit too cerebral. I told him that I wanted his job someday and that I'd like to spend some time in the president's office to watch the airline's business model in action.