No, the confounding variable does not have to be consistent with the hypothesis. It can actually give you data that would tend to disprove the hypothesis. The problem is that that data will still be flawed because it is the confounding variable that is at work. So you might end up thinking your hypothesis has been disproven when it really has not been.
Let's say that you hypothesize that Teaching Strategy A (TSA) will lead students to have better test scores in math than Teaching Strategy B (TSB). You split your subjects up into two groups, one is taught with TSA and one is taught with TSB.
Now bring in a confounding variable. Assume that all the students that were taught with TSA had 0 hours of sleep the night before while all those that were taught with TSB got a good rest. When you test your students, it may well be that the TSA students will do worse than the TSB students. This will seem to disprove your hypothesis even though it may be the lack of sleep and not TSA that is making the students do poorly.
In a case like this, a confounding variable can seem to disprove a hypothesis.