In the US a degree would have absolutely nothing to do with getting to the left seat. There are only two factors which apply:

Do you have enough seniority?
Can you pass the training?

That's it.

The degree, and all other competitive factors, come into play primarily for getting an interview, and to a lesser extent at the interview. Today most airlines WANT to hire you if they call you... you just have to prepare. they already know if you have a degree, so that's not going to be much of an interview factor if they called you in the first place.