Degrees have become so commonplace, they're another box to tick for the box tickers, so I absolutely do not believe the possessing of a degree infers some level of intelligence or any special personal qualities. So no, I don't care if a man has a degree or not. That fact doesn't tell me anything about the qualities I care about.
I have a Bachelors with a major in Philosophy. I loved studying, but I knew then and I know now it's a more or less worthless degree. I was under a lot of pressure to go to university and please my mother, so I did it. I ticked the box. It didn't please her. She wanted me to transfer to law and be a lawyer. Constantly told me my degree is worthless and a waste of time. It's still a sore spot. She still brings up being a lawyer.
I've grown up really resenting all this degree pressure and snobbism, so I don't value degrees. My mother has a bunch and she's an awful person with terrible critical thinking skills, I think shes of average intelligence at best. I know a lot of dumb ass people with degrees. English and Communication majors who can't spell and confuse common words, lawyers who know nothing about the world or anything at all outside of their narrow speciality in law and what they were forced to read and learn about at uni.
I know some brilliant people with advanced degrees doing important work, I know brilliant people with their bachelor's who are great and people with no degree who are terrific people and very successful. And often also brilliant.
I don't think it says a lot about any qualities you may bring to a personal relationship, one way or another. Or even your earning power.