If that is UNC - yes, I would like them to do well, as I like Courney Banghart as a coach - we wanted her to get strong consideration at Rutgers as a successor to CVS, but alas, it looks like that ship sailed. That was NOT the case when Sylvia was there.
I also tend to root for NC State to do ok. I am not a huge Wes Moore fan, but think he is a heck of a coach (it has to do with when Rutgers lost to Chattanooga in the NCAA's some years back) and the legacy of Kay Yow, whom we met when t he Kay Yow foundation was announced at Rutgers, in fact my wife gave her a hug as we were seated at the table she walked by as she entered the room (really, a back corner of the arena where pre-game meals were held for donors by the fundraising group, not for free).
Duke is more complicated. I rooted for them under GG, but have disliked the current coach since her days at Michigan State. If they change coaches I expect to be cool with them again.
As you can tell, in most cases I am very coach oriented in who I am likely to root for in general. Of course, I root for Arizona and Rutgers first, and most PAC and Big Ten teams in general. There are teams that I dislike because of the school, not the coach, but in general, I root for the coaches I like to do well, and for the ones I don't, not so much.