I have been toying with this question for about a week discussing it with at least one of my readers in the comments section and that is the possibility that UNC could finish the regular season undefeated. Carolina March takes up the issue citing Seth Davis who believes UNC, Memphis and Kansas can possibly get there because they each have three or fewer games on the schedule versus the top 25. Davis also questions whether going unblemished through the regular season is a good idea more on that in a minute. Anyway, I think CM hits the nail on the head when he points out the Davis theory is flawed because it bases the chances on how many games versus the top 25 they have left. The issue there is the top 25's fluidity from week to week. In fact since Davis wrote that article, UNC has added another top 25 team to the schedule in Miami.
My own thoughts on UNC possibly going undefeated in the regular season echoes something one of my professors in seminary used to ask: "It's possible, but is it probable?" I honestly believe, on paper, UNC can win every game left on the schedule at this point. That includes the game at Cameron in March. That does not mean they will win but I think their chances to win are better than their chances of losing from here until the ACC Tournament. That being said, playing in the ACC(and this era of college basketball in general) is a fickle deal. One never knows what set of events will transpire to steal a victory from the hands of a favored team.
As for the benefits of losing now to take the pressure off for later, Roy Williams is on record as saying he thinks losing a game might be the only thing that gets his guys to play better defense. We will see about that. Given it has been 32 years since anyone finished a title season with zero losses, history does not favor the team that enters their conference tournament or the NCAA Tournament undefeated. But as CM points out the odds are about the same for the one loss teams too.
In the end I say try to win them all and see what happens. Who knows, this year might be the year and UNC might be that team. It's possible, I just don't think it is probable.