Yup, root for them to lose all you want. Heck, even I (the most noted Carolina sympathizer in these here parts) root for them to lose when I am watching one of their games. I rationally think their victories are mostly good for Duke (though I rationally want them to lose enough to give Duke the ACC title) but I emotionally want them to lose.
But, I refer you back to the definition of a certain type of Duke fan that started this discussion:
I say people who are more focussed on Carolina's failure than in Duke's success are not really Duke fans. They are anti-Carolina fans who fuel their ABC feeling by rooting for the school that is Carolina's biggest rival.
For example, I imagine there are some people who would not really mind if Duke went 3-27 one season so long as those 3 victories were over UNC and Carolina went 0-30 that same year. Taken to a less ridiculous extreme, there are people who would not mind Duke finishing 5th or 6th in the ACC if Carolina finished lower than us and we beat them when we played them.
I say a person like that is not a Duke fan. Though that is just my opinion.
--Jason "Feldy, I almost didn't post in this thread because my response was so predictable... but I could not resist
" Evans