This is a good question. It is probably best to start with what the conch represents in the book, Lord of the Flies. The conch is a symbol of order. When the boys crash on the island and they are without leadership and organization, the conch is blown to bring the boys together to form a group. Hence, the conch is a symbol of society and civilization.
When the conch breaks, it is also a symbol that all order is now gone. What we see is a crumbling of society. We see the death of Simon and Piggy.
Based on this brief description, we can say that the U.S. constitution is like the conch in that it brings organization and order. There is a civilizing force in both.