No, it won’t affect adults. It’s a K-12 education reform, which is something American schools have dealt with countless times. Sometimes they stick, but usually they eventually fade away and the next reform comes about. I don’t think anyone is really expecting the Common Core to complete revolutionize education- we’ve all heard that before- but it is a pretty common sense reform and with any luck the basic ideas will stick.
There is some higher education involvement in the sense that one of the main motivations for developing the Common Core is that there is a gap between the knowledge that high school kids are graduating with and what colleges are expecting incoming freshmen to know- hence the massive numbers of students who have to take remedial classes before beginning college level work. Done right, the Common Core is meant to ensure graduates are at least on the right track towards actually being ready for university level coursework. Obviously, not every student is going to achieve that, but at least that level of education will be available to those who can manage it and hopefully nobody will be going to schools that don’t prepare anyone for college level work.
Universities at this point are pretty uninterested in the whole thing. For one, it will take a while for the effects to trickle up. Today’s high school seniors are not going to magically be transformed into higher achieving students. But maybe today’s sixth graders will. For another, universities just have a lot more pressing issues on their mind. For the most part, they take the students they take and leave the students they leave, so if everyone is achieving slightly more that’s great, but doesn’t really change much.