By sacrificing the death into Shadow's name, it seems that Laura created a significant precedent.
What's the consequence of the sacrifice dedicated to Shadow?
I don't think this is entirely clear. I'm also not sure if I should use spoiler tags here, so I will play it safe.
is Baldur, a god and son of a god. It's possible the sacrifice empowers him somewhat, though Baldur is not a god of war per se. Recall that after the battle, and after he takes the coin back from Laura, he runs into Sam Back Crow. She is with a girlfriend. He slips some flowers into her hands but neither Sam Black Crow or the other girl see Shadow. So he's "behind the scenery" as it were. Perhaps that was partly a result of the sacrifice, though this is highly speculative.