I have not presumed in my hypothesis that the actions of the people of the world are insignificant; simply that the Dragon is more relevant in a cosmic sense then may appear.

If the actions of the people were irrelevant, then Rand's answer from the Eelfinn would have had no meaning. Why unite the lands against the Dark One if it doesn't matter? Simply put: it does matter.

However, Rand's significance- the Dragon's significance- is vital to the restoration of the world. That's why the Shadow took such measures to turn him to their side. That's why the wolves were so invested in Rand's epiphany at Dragonmount. That's why the Borderlanders were charged to test him and bring about his fall quickly so the world would have its end quickly.

As Shannow quoted: the land is one with the Dragon, and the Dragon is one with the land. Examples of this are obvious. When Rand saw his darkest times, the world around him befell the worst of his Ta'veren twists. After his revelation, good luck and miracles were abound.

If Rand is in fact an incarnation of the Great Serpent, suddenly a lot of the mysticism around him is made clear. The intentions of the Shadow are also much more understandable. If Rand were just a man, ta'veren or no, Dragon Reborn or no, what is the point of turning him to the Shadow rather than just killing him?

Rand as the Great Serpent doesn't outshine the roles of the rest of the characters. What it does, though, is bring about a more level playing field between him and the Dark One. When facing an entity as vast and destructive as the Dark One, it is difficult to see how anything will stand against it. Understanding Rand's role in the universe can help see how he will be able to do just that.

You can't win a game of chess with just your pawns, nor with just your queen. All the pieces must work in concert to win.