Possible, but they'd need a fair bit of help. They've got the "started too low" problem right now.
Four Big 12 schools ahead of them in the last rankings that ALL have 2 top 15 matchups left to add to their resumes, two undefeated B1G teams and a third with 1 loss, two SEC teams with 1 loss, Notre Dame with 1 loss, etc. Some of that will take care of itself (Big XII teams play each other, SEC CCG takes care of one, etc.) but there is a lot ahead of UNC that they need moved out of the way.
That's the thing, built into the thought is the notion that teams in front will necessarily fall, because they'll be playing each other.
Ohio State will face Michigan State. One of those teams will lose and eject themselves from the conversation. MSU, with 2 losses, would be done, and it would be hard for Ohio State to recover from a loss this late in the season. Then in the CCG, Iowa will play Ohio State or Michigan State. That's a loser leave town match. Big Ten's 3 are now down to at most 1.
The Big XII. Only one can emerge, and there's still the possibility of none. This week has TCU/OU and Gondo State/Baylor, and next week is TCU/Baylor and Gondo State/OU. All are in front of UNC right now, but they'll weed themselves down to 1 contender.
Florida and Alabama are ahead of UNC right now, but they'll settle that in the CCG. Only one, at most, is getting in.
Anyway, just to bring this home, here's the AP top 12 for this week. (Let's assume the CFP is roughly this, but who knows.) Let's play the season forward with the other guys eliminating one another, and UNC beating Clemson in the ACC CCG. I'll strike through the possible eliminated, and for the purposes of this exercise, I'm just allowing the higher ranked teams to survive (other than Clemson) their gauntlets.
1 Clemson
2 Ohio State
3 Alabama
4 Oklahoma State
5 Notre Dame
6 Iowa
7 Oklahoma
8 Florida
9 Michigan State
10 Baylor
11 TCU
12 North Carolina
Based off attrition, UNC could move up to 5, and then I think it would come down to UNC versus Notre Dame, and style points versus Clemson (common head-to-head) might matter. Edit: I'd favor Notre Dame to get the nod, given their schedule versus North Carolina's, but still, it's not a difficult road to 5, at the very least.