Does Marching Matter?

Tomorrow, November 15, massive marches are planned at city halls across the state and the country to protest the passage of Prop 8 and the repudiation of gay rights in several states. While I'll definitely be in downtown LA with everyone else, I always struggle with the actual effects of marches and protests. I often hear people argue that they only alienate the more moderate and people from the other side of the fence. Have they worked well historically? It's difficult to tell when marches are generally part of much wider movements and broader-based campaigns against the establishment. But they have certainly been associated with some of the most transformative social movements of modern history. Gandhi's march to the sea, the marches for women's suffrage, civil rights, and an end to the Vietnam War in the U.S. demonstrate the power that marches can have in their own time and in the subsequent popular imagination. Alienating or not, they ultimately succeeded in winning their goal. Would so many historical movements have succeeded had the visible protest element been removed? Why else do authoritarian governments work so hard and spend so much to suppress media and information?
Does marching matter? I believe ultimately it keeps the issue in the public eye-- whether it changes any minds is debatable. But the expression of support, passion, and, in this particular instance, frustration that can be seen in the mass gathering of people doubtlessly aids the internal solidarity of the movement and preserves the energy and passion of its supporters.