A study in a recent Journal of Politics (volume 73, April 2011, pp 463-476) actually tests this assumption. And finds it wanting.
Written by five folks from Yale and one (sympathy?) author from Michigan State, the study uses a field experiment at 59 high school classrooms to find that enhanced civics classes lead to greater constitutional knowledge as compared to students in conventional civics classes. No surprise there. But unlike previous assumptions and correlational studies, it also found no increased support for civil liberties. As the authors write:
The findings imply that students can become more knowledgeable about the Constitution and workings of government without experiencing a concomitant shift in their support for free speech, dissent, or due process. This pattern of results is striking both because this experiment has ample power to detect even small effects and because, as noted above, the statistical test is biased in favor of finding a mediating relationship. The theoretical implications of this finding are profound. Evidently, it is possible to increase awareness and understanding of civil liberties without producing an increase in support for those civil liberties. This finding therefore calls into question the longstanding argument that beliefs and attitudes are causally linked in this domain.
To put this in somewhat less theoretical words -- oh crap.
The question of whether knowledge is associated with, or independent of, attitudes has been of some interest lately. Approaches such as motivated reasoning point to this separation, finding that basically people believe what they want to believe, regardless of the factual nature of, um, the facts.
The results above are more complicated than that, but they do suggest very different avenues of cognition and belief. Or, as the authors suggest, it may be that knowledge and attitudes are "casually disconnected." As they say:
One cannot increase support for civil liberties simply by teaching students about the provisions of law that are designed to protect these liberties.